As advanced undergraduate and graduate students begin conducting research, they must base their work on articles found in academic journals. However, there is often a gap between the levels at which a textbook and a journal article are written. Bridging that gap are tutorials on fundamental, yet advanced, concepts such as: (i) algorithmic details of linear and mixed integer optimizers, (ii) formulation ideas which may render models more tractable, (iii) descriptions of the mathematical structure of linear and mixed integer programs, and (iv) manuals of modeling languages, and linear and mixed integer solvers that enable quick implementation of formulations, and the solution of the corresponding mathematical model instance. In this survey pa...