The Bertini software package provides a powerful toolset for the numerical solution of systems of polynomial equations. This book provides both a course, with numerous examples, on the use of Bertini to compute solutions, and a complete reference guide with documentation on syntax and usage options. It describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. This book serves scientists and engineers who need quick methods for finding isolated solutions to small systems. Those who wish to further refine their techniques can advance to using algorithms for finding positive-dimensional solution sets and learn how to use parallel computers on large problems, while readers of a more mathematical bent will find details of the theory underpinning the software.