diff --git a/src/bignum.c b/src/bignum.c
index d7637b1..07099d4 100644
--- a/src/bignum.c
+++ b/src/bignum.c
@@ -18,6 +18,9 @@
 
 // Internal methods
 static bigint_result_t bigint_trim_zeros(bigint_t *number);
+static bigint_result_t bigint_compare_abs(const bigint_t *x, const bigint_t *y);
+static bigint_result_t bigint_add_abs(const bigint_t *x, const bigint_t *y);
+static bigint_result_t bigint_sub_abs(const bigint_t *x, const bigint_t *y);
 
 /**
  * bigint_from_int
@@ -104,7 +107,6 @@ static bigint_result_t bigint_trim_zeros(bigint_t *number) {
         vector_result_t get_res = vector_get(number->digits, number_len - 1);
         if (get_res.status != VECTOR_OK) {
             vector_destroy(number->digits);
-            free(number);
             result.status = BIGNUM_ERR_INVALID;
             COPY_MSG(result, get_res.message);
 
@@ -119,7 +121,6 @@ static bigint_result_t bigint_trim_zeros(bigint_t *number) {
         vector_result_t pop_res = vector_pop(number->digits);
         if (pop_res.status != VECTOR_OK) {
             vector_destroy(number->digits);
-            free(number);
             result.status = BIGNUM_ERR_INVALID;
             COPY_MSG(result, get_res.message);
 
@@ -132,7 +133,6 @@ static bigint_result_t bigint_trim_zeros(bigint_t *number) {
         vector_result_t get_res = vector_get(number->digits, number_len - 1);
         if (get_res.status != VECTOR_OK) {
             vector_destroy(number->digits);
-            free(number);
             result.status = BIGNUM_ERR_INVALID;
             COPY_MSG(result, get_res.message);
 
@@ -152,6 +152,437 @@ static bigint_result_t bigint_trim_zeros(bigint_t *number) {
 
 }
 
+/**
+ * bigint_compare_abs
+ *  @x: a non-null big integer
+ *  @y: a non-null big integer
+ *
+ *  Compares absolute value of two big integers
+ *  if |x| < |y| => -1
+ *  if |x| == |y| => 0
+ *  if |x| > |y| => 1
+ *
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_compare_abs(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+
+    const size_t x_size = vector_size(x->digits);
+    const size_t y_size = vector_size(y->digits);
+
+    if (x_size != y_size) {
+        result.value.compare_status = (x_size > y_size) ? 1 : -1;
+        result.status = BIGNUM_OK;
+        SET_MSG(result, "Big integer comparison was successful");
+
+        return result;
+    }
+
+    // Start to compare from the MSB
+    for (int idx = (x_size - 1); idx >= 0; idx--) {
+        vector_result_t x_get = vector_get(x->digits, idx);
+        if (x_get.status != VECTOR_OK) {
+            vector_destroy(x->digits);
+            vector_destroy(y->digits);
+            result.status = BIGNUM_ERR_INVALID;
+            COPY_MSG(result, x_get.message);
+
+            return result;
+        }
+
+        vector_result_t y_get = vector_get(y->digits, idx);
+        if (y_get.status != VECTOR_OK) {
+            vector_destroy(x->digits);
+            vector_destroy(y->digits);
+            result.status = BIGNUM_ERR_INVALID;
+            COPY_MSG(result, y_get.message);
+
+            return result;
+        }
+
+        int *x_digit = (int*)x_get.value.element;
+        int *y_digit = (int*)y_get.value.element;
+
+        if (*x_digit != *y_digit) {
+            result.value.compare_status = (*x_digit > *y_digit) ? 1 : -1;
+            result.status = BIGNUM_OK;
+            SET_MSG(result, "Big integer comparison was successful");
+
+            return result;
+        }
+    }
+
+    result.value.compare_status = 0;
+    result.status = BIGNUM_OK;
+    SET_MSG(result, "Big integer comparison was successful");
+
+    return result;
+}
+
+/**
+ * bigint_compare
+ *  @x: a valid non-null big integer
+ *  @y: a valid non-null big integer
+ * 
+ *  Compares two big integers
+ *  if x < y => -1
+ *  if x == y => 0
+ *  if x > y => 1
+ * 
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_compare(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+
+    if (x->is_negative != y->is_negative) {
+        result.value.compare_status = x->is_negative ? -1 : 1;
+        result.status = BIGNUM_OK;
+        SET_MSG(result, "Big integer comparison was successful");
+
+        return result;
+    }
+    
+    bigint_result_t cmp_res = bigint_compare_abs(x, y);
+    if (cmp_res.status != BIGNUM_OK) {
+        vector_destroy(x->digits);
+        vector_destroy(y->digits);
+
+        return cmp_res;
+    }
+    
+    const uint8_t abs_cmp = cmp_res.value.compare_status;
+
+    result.value.compare_status = x->is_negative ? -abs_cmp : abs_cmp;
+    result.status = BIGNUM_OK;
+    SET_MSG(result, "Big integer comparison was successful");
+
+    return result;
+}
+
+/**
+ * bigint_add_abs
+ *  @x: a non-null big integer
+ *  @y: a non-null big integer
+ * 
+ *  Adds two absolute values together
+ * 
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_add_abs(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+
+    bigint_t *sum = malloc(sizeof(bigint_t));
+    if (sum == NULL) {
+        result.status = BIGNUM_ERR_ALLOCATE;
+        SET_MSG(result, "Cannot allocate memory for big integer");
+
+        return result;
+    }
+
+    const size_t max_size = vector_size(x->digits) > vector_size(y->digits) ?
+                            vector_size(x->digits) : vector_size(y->digits);
+
+    vector_result_t vec_res = vector_new(max_size + 1, sizeof(int));
+    if (vec_res.status != VECTOR_OK) {
+        free(sum);
+        result.status = BIGNUM_ERR_INVALID;
+        COPY_MSG(result, vec_res.message);
+
+        return result;
+    }
+
+    sum->digits = vec_res.value.vector;
+    sum->is_negative = false;
+
+    long long carry = 0;
+    size_t idx = 0;
+
+    while (idx < vector_size(x->digits) || idx < vector_size(y->digits) || carry) {
+        long long partial_sum = carry;
+
+        if (idx < vector_size(x->digits)) {
+            vector_result_t get_res = vector_get(x->digits, idx);
+            if (get_res.status != VECTOR_OK) {
+                vector_destroy(sum->digits);
+                free(sum);
+                result.status = BIGNUM_ERR_INVALID;
+                COPY_MSG(result, get_res.message);
+
+                return result;
+            }
+
+            int *x_digit = (int*)get_res.value.element;
+            partial_sum += *x_digit;
+        }
+
+        if (idx < vector_size(y->digits)) {
+            vector_result_t get_res = vector_get(y->digits, idx);
+            if (get_res.status != VECTOR_OK) {
+                vector_destroy(sum->digits);
+                free(sum);
+                result.status = BIGNUM_ERR_INVALID;
+                COPY_MSG(result, get_res.message);
+
+                return result;
+            }
+
+            int *y_digit = (int*)get_res.value.element;
+            partial_sum += *y_digit;
+        }
+
+        int digit = partial_sum % BIGINT_BASE;
+        carry = partial_sum / BIGINT_BASE;
+
+        vector_result_t push_res = vector_push(sum->digits, &digit);
+        if (push_res.status != VECTOR_OK) {
+            vector_destroy(sum->digits);
+            free(sum);
+            result.status = BIGNUM_ERR_INVALID;
+            COPY_MSG(result, push_res.message);
+
+            return result;
+        }
+        idx++;
+    }
+
+    bigint_result_t trim_res = bigint_trim_zeros(sum);
+    if (trim_res.status != BIGNUM_OK) {
+        vector_destroy(sum->digits);
+        free(sum);
+        
+        return trim_res;
+    }
+
+    result.value.number = sum;
+    result.status = BIGNUM_OK;
+    SET_MSG(result, "Big integers successfully added");
+
+    return result;
+}
+
+/**
+ * bigint_sub_abs
+ *  @x: a non-null big integer
+ *  @y: a non-null big integer
+ * 
+ *  Subtracts two absolute values assuming that |x| >= |y|
+ * 
+ *  Returns a bigint_result_t data type
+ */
+bigint_result_t bigint_sub_abs(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+
+    bigint_t *difference = malloc(sizeof(bigint_t));
+    if (difference == NULL) {
+        result.status = BIGNUM_ERR_ALLOCATE;
+        SET_MSG(result, "Cannot allocate memory for big integer");
+
+        return result;
+    }
+
+    vector_result_t vec_res = vector_new(vector_size(x->digits), sizeof(int));
+    if (vec_res.status != VECTOR_OK) {
+        free(difference);
+        result.status = BIGNUM_ERR_INVALID;
+        COPY_MSG(result, vec_res.message);
+
+        return result;
+    }
+
+    difference->digits = vec_res.value.vector;
+    difference->is_negative = false;
+
+    long long borrow = 0;
+
+    for (size_t idx = 0; idx < vector_size(x->digits); idx++) {
+        vector_result_t x_get_res = vector_get(x->digits, idx);
+        if (x_get_res.status != VECTOR_OK) {
+            vector_destroy(difference->digits);
+            free(difference);
+            result.status = BIGNUM_ERR_INVALID;
+            COPY_MSG(result, x_get_res.message);
+
+            return result;
+        }
+
+        int *x_digit = (int*)x_get_res.value.element;
+        long long partial_difference = *x_digit - borrow;
+
+        if (idx < vector_size(y->digits)) {
+            vector_result_t y_get_res = vector_get(y->digits, idx);
+            if (y_get_res.status != VECTOR_OK) {
+                vector_destroy(difference->digits);
+                free(difference);
+                result.status = BIGNUM_ERR_INVALID;
+                COPY_MSG(result, y_get_res.message);
+
+                return result;
+            }
+
+            int *y_digit = (int*)y_get_res.value.element;
+            partial_difference -= *y_digit;
+        }
+
+        if (partial_difference < 0) {
+            partial_difference += BIGINT_BASE;
+            borrow = 1;
+        } else {
+            borrow = 0;
+        }
+
+        int digit = partial_difference;
+        vector_result_t push_res = vector_push(difference->digits, &digit);
+        if (push_res.status != VECTOR_OK) {
+            vector_destroy(difference->digits);
+            free(difference);
+            result.status = BIGNUM_ERR_INVALID;
+            COPY_MSG(result, push_res.message);
+
+            return result;
+        }
+    }
+
+    bigint_result_t trim_res = bigint_trim_zeros(difference);
+    if (trim_res.status != BIGNUM_OK) {
+        vector_destroy(difference->digits);
+        free(difference);
+        
+        return trim_res;
+    }
+
+    result.value.number = difference;
+    result.status = BIGNUM_OK;
+    SET_MSG(result, "Big integers successfully subtracted");
+
+    return result;
+}
+
+/**
+ * bigint_add
+ *  @x: a non-null big integer
+ *  @y: a non-null big integer
+ * 
+ *  Adds two big integers together
+ * 
+ *  Returns a bigint_result_t data type 
+ */
+bigint_result_t bigint_add(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+
+    if (x == NULL || y == NULL) {
+        result.status = BIGNUM_ERR_INVALID;
+        SET_MSG(result, "Invalid big integers");
+
+        return result;
+    }
+
+    // Same sign: add absolute values
+    if (x->is_negative == y->is_negative) {
+        bigint_result_t sum_res = bigint_add_abs(x, y);
+        if (sum_res.status != BIGNUM_OK) {
+            return sum_res;
+        }
+
+        bigint_t *sum = sum_res.value.number;
+        if (sum) {
+            sum->is_negative = x->is_negative;
+        }
+
+        result.value.number = sum;
+        result.status = BIGNUM_OK;
+        SET_MSG(result, "Big integers successfully added");
+
+        return result;
+    }
+
+    // Different signs: subtract smaller from larger
+    bigint_result_t cmp_res = bigint_compare_abs(x, y);
+    if (cmp_res.status != BIGNUM_OK) {
+        return cmp_res;
+    }
+    
+    const uint8_t cmp = cmp_res.value.compare_status;
+    if (cmp == 0) {
+        return bigint_from_int(0);
+    } else if (cmp > 0) {
+        bigint_result_t sub_res = bigint_sub_abs(x, y);
+        if (sub_res.status != BIGNUM_OK) {
+            return sub_res;
+        }
+
+        bigint_t *sub = sub_res.value.number;
+        if (sub) {
+            sub->is_negative = x->is_negative;
+        }
+
+        result.value.number = sub;
+        result.status = BIGNUM_OK;
+        SET_MSG(result, "Big integers successfully added");
+    } else {
+        bigint_result_t sub_res = bigint_sub_abs(y, x);
+        if (sub_res.status != BIGNUM_OK) {
+            return sub_res;
+        }
+        
+        bigint_t *sub = sub_res.value.number;
+        if (sub) {
+            sub->is_negative = y->is_negative;
+        }
+
+        result.value.number = sub;
+        result.status = BIGNUM_OK;
+        SET_MSG(result, "Big integers successfully added");
+    }
+
+    return result;
+}
+
+/**
+ * bigint_sub
+ *  @x: a non-null big integer
+ *  @y: a non-null big integer
+ * 
+ *  Subtracts two big integers together
+ * 
+ *  Returns a bigint_result_t data type 
+ */
+bigint_result_t bigint_sub(const bigint_t *x, const bigint_t *y) {
+    bigint_result_t result = {0};
+
+    if (x == NULL || y == NULL) {
+        result.status = BIGNUM_ERR_INVALID;
+        SET_MSG(result, "Invalid big integers");
+
+        return result;
+    }
+
+    /* To subtract two big integers we can consider
+     * the following equivalence:
+     * x - y = x + (-y) 
+     */
+    bigint_result_t neg_y_res = bigint_clone(y);
+    if (neg_y_res.status != BIGNUM_OK) {
+        return neg_y_res;
+    }
+    
+    bigint_t *neg_y = neg_y_res.value.number;
+    neg_y->is_negative = !neg_y->is_negative;
+
+    bigint_result_t difference_res = bigint_add(x, neg_y);
+    if (difference_res.status != BIGNUM_OK) {
+        return difference_res;
+    }
+    
+    bigint_destroy(neg_y);
+    bigint_t *difference = difference_res.value.number;
+
+    result.value.number = difference;
+    result.status = BIGNUM_OK;
+    SET_MSG(result, "Big integers successfully subtracted");
+
+    return result;
+}
+
 /**
  * bigint_from_string
  *  @string_num: an array of chars representing a number
@@ -236,7 +667,13 @@ bigint_result_t bigint_from_string(const char *string_num) {
         }
     }
 
-    bigint_trim_zeros(number);
+    bigint_result_t trim_res = bigint_trim_zeros(number);
+    if (trim_res.status != BIGNUM_OK) {
+        vector_destroy(number->digits);
+        free(number);
+
+        return trim_res;
+    }
 
     result.status = BIGNUM_OK;
     SET_MSG(result, "Big integer successfully created");
@@ -244,9 +681,51 @@ bigint_result_t bigint_from_string(const char *string_num) {
     return result;
 }
 
+/**
+ * bigint_clone
+ *  @number: a valid non-null big integer
+ *  
+ *  Clones a big integer
+ * 
+ *  Returns a bigint_result_t data type containing the new big integer
+ */
+bigint_result_t bigint_clone(const bigint_t *number) {
+    bigint_result_t result = {0};
+
+    if (number == NULL) {
+        result.status = BIGNUM_ERR_INVALID;
+        SET_MSG(result, "Invalid big integer");
+
+        return result;
+    }
+
+    bigint_t *cloned = malloc(sizeof(bigint_t));
+    if (cloned == NULL) {
+        result.status = BIGNUM_ERR_ALLOCATE;
+        SET_MSG(result, "Failed to allocate memory for big integer");
+
+        return result;
+    }
+
+    vector_result_t vec_res = vector_new(vector_size(number->digits), sizeof(int));
+    if (vec_res.status != VECTOR_OK) {
+        free(cloned);
+        result.status = BIGNUM_ERR_ALLOCATE;
+        COPY_MSG(result, vec_res.message);
+
+        return result;
+    }
+
+    result.value.number = cloned;
+    result.status = BIGNUM_OK;
+    SET_MSG(result, "Big integer successfully cloned");
+
+    return result;
+}
+
 /**
  * bigint_destroy
- *  @number: a valid big integer
+ *  @number: a valid non-null big integer
  * 
  *  Deletes the big integer from the memory
  *  
diff --git a/src/bignum.h b/src/bignum.h
index 07de64b..3a4fd55 100644
--- a/src/bignum.h
+++ b/src/bignum.h
@@ -30,6 +30,7 @@ typedef struct {
     uint8_t message[RESULT_MSG_SIZE];
     union {
         bigint_t *number;
+        uint8_t compare_status;
         char *string_num;
     } value;
 } bigint_result_t;
@@ -40,6 +41,10 @@ extern "C" {
 
 bigint_result_t bigint_from_int(long long value);
 bigint_result_t bigint_from_string(const char *string_num);
+bigint_result_t bigint_clone(const bigint_t *number);
+bigint_result_t bigint_compare(const bigint_t *x, const bigint_t *y);
+bigint_result_t bigint_add(const bigint_t *x, const bigint_t *y);
+bigint_result_t bigint_sub(const bigint_t *x, const bigint_t *y);
 bigint_result_t bigint_destroy(bigint_t *number);
 
 #ifdef __cplusplus