Dedicated to William T. Beale (1928 - 2016), inventor of the Free Piston Stirling Engine, Mentor and Frien. This web resource is intended to be totally self contained learning resource for the analysis and development of computer simulation of single phase, piston/cylinder Stirling cycle machines. It includes thermodynamic, heat transfer and fluid flow friction analysis, and until 2012 it was used as resource material for an advanced course for Mechanical Engineering majors. The course structure was based on the book by I.Urieli & D.M.Berchowitz 'Stirling Cycle Engine Analysis' (Adam Hilger, 1984). The computer simulation program modules (originally written in FORTRAN) have all been updated and rewritten in MATLAB, a convenient interactive language which allows direct graphical output - essential for Stirling cycle analysis. A complete set of all the m-files are developed and provided, and they can be augmented and adapted as needed for specific engine/refrigerator configurations. It is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license and as such is freely available. Comments and constructive criticism are welcomed by the author. Chapter 1: Background and Introduction Chapter 2: Basic Engine Configurations Chapter 3: Ideal Isothermal Analysis We define and analyze the Ideal Isothermal model of a Stirling engine, including the Schmidt Analysis, and discuss its limitations. One obviously incorrect conclusion of this analysis is that all three heat exchangers are redundant, and only contribute dead space, since all required heat transfer processes occur in the isothermal compression and expansion spaces. Nevertheless we can obtain a better understanding of a specific design, particularly when we augment the solution with Allan Organ's particle mass flow analysis. Chapter 4: Ideal Adiabatic Analysis We find that the Ideal Isothermal analysis predicts that the heat exchangers of a Stirling engine are redundant, thus we cannot seriously use this model to predict the ideal performance of an actual machine. We thus turn to an alternative model in which the compression and expansion spaces are adiabatic. We find that there is no closed form solution to this model and we have to resort to computer simulation. We gain various insights from using this model in particular with regards to the importance of the regenerator, which was not understood for a significant period. Chapter 5: Simple Analysis This analysis approach uses the Ideal Adiabatic model as a basis to predict the real performance of the three heat exchanger sections, particularly with regards to heat transfer and