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This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.

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1 Diffusion.- 2 The Laplace equation.- 3 First order equations.- 4 Waves.- 5 Functional analysis.- 6 Variational formulations.- 7 Appendix A Sturm-Liouville, Legendre and Bessel equations.- 8 Appendix B Identities.

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"The material, at an advanced undergraduate or first year graduate level, presents a very interesting mix of physical applications and abstract theory supporting rigorous existence and regularity results of PDEs. ... Each chapter begins with a short formal summary of the basic concepts, which is followed by several dozen of problems covering all aspects of the materials in the corresponding chapters of the book." (Peter Bernard Weichman, Mathematical Reviews, July, 2016)

"Provides an excellent overview of the field and is highly recommended for modern PDEs courses designed for advanced students. ... Each chapter first reviews the main theoretical concepts and tools and then provides solved problems and exercises. A broad range of problems and exercises at various levels of difficulty, as well as the extensive reference list, makes this book a valuable resource for advanced undergraduate or beginning graduate researchers ... . Summing Up: Highly recommended. Upper-division undergraduates, graduate students, researchers/faculty." (C. Park, Choice, Vol. 53 (9), May, 2016)

"The authors´ aim is to give a systematic treatment of some of the classical methods in partial differential equations. ... the book is a very useful contribution to the growing literature on this circle of ideas. I wholeheartedly recommend this book both as a textbook, as well as for independent study." (Vicentiu D. Radulescu, zbMATH 1330.35003, 2016)

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Prof. Sandro Salsa and Prof. Gianmaria Verzini, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy.

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