GAMS (General Algebraic Modeling System) is a high-level programming language that allows users to define and solve optimization problems. It has been widely used in various fields, including economics, engineering, and science. This guide will provide an overview of GAMS, how to write the language, an example of a simple GAMS program, and some of its best applications.

What is GAMS?
GAMS was developed in the 1970s by the GAMS Development Corporation, and it has since become a popular language for mathematical modeling and optimization. GAMS allows users to express complex mathematical models in a concise and readable form. It also provides a suite of optimization solvers to solve the models efficiently.

Writing GAMS
GAMS programs consist of a series of statements that describe the problem to be solved. The statements are written in a syntax that resembles mathematical notation. The basic structure of a GAMS program is as follows:

```
$TITLE My GAMS Program
$MODELTYPE Optimization
$OBJECTIVE Objective Function

* Sets
Set i /1*5/
    j /1*3/;

* Parameters
Parameter A(i,j)
    B(i)
    C(j);

* Variables
Variable X(i,j);

* Objective Function
Equation Obj;
Obj.. sum((i,j), X(i,j)) =E= z;

* Constraints
Equation Con1(i);
Con1(i).. sum(j, A(i,j)*X(i,j)) =L= B(i);

Equation Con2(j);
Con2(j).. sum(i, C(j)*X(i,j)) =L= d(j);
```

The program consists of several sections, including sets, parameters, variables, and constraints. These sections are used to define the problem to be solved. The objective function and constraints are also defined using equations. The syntax of GAMS is quite intuitive, and it can be learned quickly with some practice.

Example GAMS Program
Here is a simple example of a GAMS program that solves a linear programming problem:

```
$TITLE Linear Programming Example
$MODELTYPE LP
$OFFLISTING

* Sets
Set i /1*3/;
Set j /1*2/;

* Parameters
Parameter A(i,j) /1 2, 3 4, 5 6/;
Parameter B(i) /10, 20, 30/;
Parameter C(j) /7, 8/;

* Variables
Variable X(j);

* Objective Function
Equation Obj;
Obj.. sum(j, C(j)*X(j)) =E= z;

* Constraints
Equation Con1(i);
Con1(i).. sum(j, A(i,j)*X(j)) =L= B(i);

* Solve the Model
Model LPModel /Obj, Con1/;
Solve LPModel using LP maximizing z;
```

This program defines a simple linear programming problem with two decision variables and three constraints. The program solves the problem using the LP solver and maximizes the objective function.

Best Applications for GAMS
GAMS has been used in various fields, including economics, engineering, and science. Some of the best applications of GAMS include:

1. Energy System Modeling: GAMS has been used to model energy systems and optimize energy generation and consumption.

2. Transportation Planning: GAMS has been used to model transportation networks and optimize routing and scheduling.

3. Economic Modeling: GAMS has been used to model economic systems and optimize economic policies.

4. Environmental Modeling: GAMS has been used to model environmental systems and optimize environmental policies.

Conclusion
GAMS is a powerful language for mathematical modeling and optimization. It allows users to express complex problems in a concise and readable form, making it easy to develop and solve optimization models. Writing GAMS is straightforward, and it can be learned quickly with some practice. The example program provided above demonstrates the basic structure of a GAMS program and how it can be used to solve a simple linear programming problem. Finally, GAMS has been widely used in various fields, making it a versatile tool for solving complex optimization problems.