This is a handbook for scientists, engineers and those intersted in mathematics and its applications. It presents a brief history of mathematics followed by a summary of basic undergraduate methods, techniques and formulas together with numerous fi gures and examples. Within the text is a summary of the basic formulas from algebra, trigonometry, plane geometry, solid geometry, calculus, vector calculus, ordinary differential equations, probability and statistics along with diagrams and illustrations showing how formulas are to be applied. This is followed by a chapter on special functions which arise in a variety of mathematics applications. The fi nal chapter is a collection of selected applied mathematics applications taken from the subject areas of mechanics, physics and chemistry. There are three appendices. The appendix A contains units of measurement from the Système International d' Unitès (designated SI in all Languages). The appendix B contains tables of integrals for both indefi nite and defi nite integrals, with over 850 integrals presented. The appendix C contains miscellaneous topics that students entering the fi elds of science or engineering should be aware of. There is also an extensive index to aid in fi nding information about a specifi c topic. This handbook presents a summary of selected mathematics topics from college/university level mathematics courses. Fundamental principles are reviewed and presented by way of examples, fi gures, tables and diagrams. It condenses and presents under one cover basic concepts from several different applied mathematics topics. The following topics are examined: History of mathematics Geometry Algebra and Trigonometry Calculus and Vector Calculus Ordinary Differential Equations Probability and Statistics Selected topics from Physics and Chemistry Selected applied mathematics topics Numerous applications of mathematics Special functions Numerical Methods Table of integrals Syst`eme International d'Unit`es