This textbook introduces the reader to specific techniques and terms of analysis that help simplify and understand complex quantitative relationships. It is primarily aimed at computer science students, but it also serves as a welcome supplementary introduction for mathematics and physics students interested in discrete structures, covering fundamental analytical tools such as estimation, approximation, and asymptotics. Notable features of the presentation include (a) an emphasis on idea formation and argument hierarchies (from graphics to proof), (b) the use of computer algebra systems for purely computational tasks, (c) the repeated exploration of examples with refined techniques and altered perspectives, and (d) motivation through problems from computer science. The book is accompanied by a hyperlinked PDF version.