diff --git a/Mathematics/README.md b/Mathematics/README.md
index 471d62c..63747d2 100644
--- a/Mathematics/README.md
+++ b/Mathematics/README.md
@@ -1 +1,93 @@
-A mathematical library smart contract
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+# Enhanced Math Library in Clarity
+
+## Overview
+
+This smart contract implements an enhanced math library in Clarity, providing a set of mathematical functions with built-in error handling and overflow/underflow protection. The library is designed to be used in other Clarity smart contracts that require safe and reliable mathematical operations.
+
+## Functions
+
+### 1. add(a int, b int) → (response int uint)
+Adds two integers with overflow protection.
+- Returns `(ok result)` if the addition is successful.
+- Returns `(err u"Overflow occurred in addition")` if an overflow occurs.
+
+### 2. subtract(a int, b int) → (response int uint)
+Subtracts two integers with underflow protection.
+- Returns `(ok result)` if the subtraction is successful.
+- Returns `(err u"Underflow occurred in subtraction")` if an underflow occurs.
+
+### 3. multiply(a int, b int) → (response int uint)
+Multiplies two integers with overflow protection.
+- Returns `(ok result)` if the multiplication is successful.
+- Returns `(err u"Overflow occurred in multiplication")` if an overflow occurs.
+
+### 4. divide(a int, b int) → (response int uint)
+Divides two integers with error handling for division by zero.
+- Returns `(ok result)` if the division is successful.
+- Returns `(err u"Cannot divide by zero")` if attempting to divide by zero.
+
+### 5. square(a int) → (response int uint)
+Calculates the square of an integer using the `multiply` function.
+- Returns `(ok result)` if the calculation is successful.
+- Returns an error if an overflow occurs during multiplication.
+
+### 6. modular(a int, b int) → (response int uint)
+Calculates the modulus of two integers with error handling for modulo by zero.
+- Returns `(ok result)` if the modulo operation is successful.
+- Returns `(err u"Cannot perform modulo by zero")` if attempting to perform modulo by zero.
+
+### 7. absolute(a int) → (response int uint)
+Calculates the absolute value of an integer.
+- Always returns `(ok result)` with the absolute value.
+
+### 8. average(a int, b int) → (response int uint)
+Calculates the average of two integers with overflow protection.
+- Returns `(ok result)` if the average calculation is successful.
+- Returns `(err u"Overflow occurred while calculating average")` if an overflow occurs during the calculation.
+
+### 9. maximum(a int, b int) → (response int uint)
+Returns the maximum of two integers.
+- Always returns `(ok result)` with the larger of the two input values.
+
+### 10. is-even(a int) → (response bool uint)
+Checks if an integer is even.
+- Returns `(ok true)` if the input is even.
+- Returns `(ok false)` if the input is odd.
+
+## Usage
+
+To use this library in your Clarity smart contract, you can either:
+
+1. Copy the functions you need directly into your contract.
+2. Deploy this contract separately and call its functions from your contract using inter-contract calls.
+
+Example usage:
+
+```clarity
+(use-trait math-lib .math-library.math-trait)
+
+(define-public (example-function (math-contract <math-lib>))
+  (let
+    (
+      (sum (contract-call? math-contract add 5 3))
+      (product (contract-call? math-contract multiply 4 7))
+    )
+    (match sum
+      success (match product
+        success (ok {sum: success, product: success})
+        error (err error))
+      error (err error))))
+```
+
+## Error Handling
+
+All functions in this library return a `response` type, which allows for proper error handling in the calling contract. Always use `match` expressions to handle both successful and error cases when calling these functions.
+
+## Limitations
+
+- This library operates on Clarity's `int` type, which has a fixed size. Be aware of the maximum and minimum values that can be represented.
+- The overflow and underflow checks may not catch all possible cases, especially for extreme values close to the limits of the `int` type.
+
+## Security Considerations
+
+While this library provides basic overflow and underflow protection, it's crucial to thoroughly test your contract with a wide range of inputs, including edge cases, before deploying it to a live network.
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diff --git a/Mathematics/contracts/mlib.clar b/Mathematics/contracts/mlib.clar
index fdbde04..645c404 100644
--- a/Mathematics/contracts/mlib.clar
+++ b/Mathematics/contracts/mlib.clar
@@ -1,15 +1,64 @@
+;; Enhanced Math Library in Clarity
 
-;; mlib
-;; <add a description here>
+;; Addition Function with overflow check
+(define-read-only (add (a int) (b int))
+  (let ((result (+ a b)))
+    (if (and (>= result a) (>= result b))
+        (ok result)
+        (err u"Overflow occurred in addition"))))
 
-;; constants
-;;
+;; Subtraction Function with underflow check
+(define-read-only (subtract (a int) (b int))
+  (let ((result (- a b)))
+    (if (or (and (>= a b) (>= result 0)) (and (< a b) (<= result 0)))
+        (ok result)
+        (err u"Underflow occurred in subtraction"))))
 
-;; data maps and vars
-;;
+;; Multiplication Function with overflow check
+(define-read-only (multiply (a int) (b int))
+  (let ((result (* a b)))
+    (if (or (is-eq b 0) (is-eq (/ result b) a))
+        (ok result)
+        (err u"Overflow occurred in multiplication"))))
 
-;; private functions
-;;
 
-;; public functions
-;;
+;; Division Function with error handling
+(define-read-only (divide (a int) (b int))
+  (if (is-eq b 0)
+      (err u"Cannot divide by zero")
+      (ok (/ a b))))
+
+;; Square Function
+(define-read-only (square (a int))
+  (multiply a a))
+
+;; Modular Function (renamed to avoid conflict with built-in 'mod' function)
+(define-read-only (modular (a int) (b int))
+  (if (is-eq b 0)
+      (err u"Cannot perform modulo by zero")
+      (ok (mod a b))))
+
+;; Absolute Value Function
+(define-read-only (absolute (a int))
+  (if (< a 0)
+      (ok (- a))
+      (ok a)))
+
+;; Average Function with overflow protection
+(define-read-only (average (a int) (b int))
+  (let 
+    (
+      (sum (add a b))
+      (half (/ (+ a b) 2))
+    )
+    (match sum
+      success (ok half)
+      error (err u"Overflow occurred while calculating average"))))
+
+;; Maximum Function
+(define-read-only (maximum (a int) (b int))
+  (ok (if (>= a b) a b)))
+
+;; Is Even Function
+(define-read-only (is-even (a int))
+  (ok (is-eq (mod a 2) 0)))
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