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One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us a sense of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems. The main goals of this book are to: -introduce the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces, -aim the text at graduate students and researchers who have a foundation in Banach space theory, - expose the reader to some current avenues of research in biorthogonal systems in Banach spaces, -provide notes and exercises related to the topic, suggest open problems and possible new directions of research. Numerous exercises are included, and the only prerequisites are a basic background in functional analysis.