Excursions in Classical Analysis introduces undergraduate students to advanced problem solving and undergraduate research in two ways. Firstly, it provides a colourful tour of classical analysis which places a wide variety of problems in their historical context. Secondly, it helps students gain an understanding of mathematical discovery and proof. In demonstrating a variety of possible solutions to the same sample exercise, the reader will come to see how the connections between apparently inapplicable areas of mathematics can be exploited in problem-solving. This book will serve as excellent preparation for participation in mathematics competitions, as a valuable resource for undergraduate mathematics reading courses and seminars and as a supplement text in a course on analysis. It can also be used in independent study, since the chapters are free-standing.