The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples.

The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. This is a textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author. Problems and solutions have been included, Appendix G has been added, more details have been presented, recent publications on evaluating Feynman integrals have been taken into account and the bibliography has been updated. The book characterizes the most powerful methods and illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples. Feynman Integral Calculus explains how the problem of evaluation has become ever more important since what could be easily evaluated has already been evaluated years ago. It demonstrates and explains how to perform the newest important calculations, while showing how to choose adequate methods and combine evaluation methods in a non-trivial way.

Feynman Integrals: Basic Definitions and Tools.- Evaluating by Alpha and Feynman Parameters.- Evaluating by MB Representation.- IBP and Reduction to Master Integrals.- Reduction to Master Integrals by Baikov's Method.- Evaluation by Differential Equations.- Tables.- Some Special Functions.- Summation Formulae.- Table of MB Integrals.- Analysis of Convergence and Sector Decompositions.- A Brief Review of Some Other Methods.- Applying Gröbner Bases to Solve IBP Relations.- Solutions.