The ideal cycle for a simple gas turbine is the Brayton Cycle, also called the Joule Cycle. In this course material, the open, simple Brayton Cycle used for stationary power generation and combustion are presented. When dealing with Brayton Cycle, air, argon, helium and nitrogen are considered as the working fluid. When dealing with combustion, six different fuels (carbon, hydrogen, sulfur, coal, oil and gas) react with air and oxygen enriched air as the oxidant at different stoichiometry values (stoichiometry => 1) and oxidant inlet temperature values. For Brayton Cycle, thermal efficiency derivation is presented with a simple mathematical approach. Also, a T - s diagram and power cycle major performance trends (thermal efficiency, specific power output, power output, combustion products composition on weight and mole basis, specific fuel consumption and stoichiometry) are plotted in a few figures as a function of compression ratio, turbine inlet temperature and/or final combustion temperature and working fluid mass flow rate. It should be noted that this course material does not deal with costs (capital, operational or maintenance). The combustion technical performance at stoichiometry => 1 conditions is presented knowing the specifc enthalpy values for combustion reactants and products, given as a function of temperature. Combustion products composition on both weight and mole basis is given in tabular form and plotted in a few figures. Also, flame temperature, oxidant to fuel ratio and fuel higher heating value (HHV) are presented in tabular form and plotted in a few figures. The provided output data and plots allow one to determine the major combustion performance laws and trends. In this course material, the student gets familiar with the ideal Brayton Cycle and combustion and their T - s and h - T diagrams, operation and major performance trends.