Cicogna, Giampaolo Mathematical methods in physics. (Metodi matematici della fisica.) (Italian) Zbl 1157.00008 Unitext; Collana di Fisica e Astronomia. Berlin: Springer (ISBN 978-88-470-0833-5/pbk). x, 242 p. (2008). This book introduces the reader to the basic and relevant mathematical structures of theoretical physics (at a level of rigor suitable to physicists). It covers some subject one needs to begin a serious graduate study in theoretical physics, mainly linear vector spaces of finite dimensions, Hilbert spaces, functions of a complex variable, Fourier and Laplace transforms and distributions. In addition to these basic issues, is presented in an Appendix, a brief introduction to the first notions of group theory and properties of symmetry.The book does not assume prior knowledge of the topics covered. However, the reader will find use of prior knowledge in linear algebra and advanced calculus (perhaps a bit of analysis). The treatment of each subject is framed in a way that makes immediate application to physics natural and intuitive. Each chapter is presented mainly in easily digestible, short sections. The only objection that may be raised is the lack of exercises intended to test and reinforce the reader’s understanding of the material covered (a failure that can be resolved in a future edition). Nevertheless, this volume is a welcome addition to the good books in this area. In summary, this book can be regarded as a good preparation for further reading such as the works of Reed/Simon (1980; Zbl 0459.46001) and Blanchard/Brüning (2002; Zbl 1019.46001). Reviewer: Daniel H. T. Franco (Belo Horizonte) Cited in 1 Review MSC: 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) 46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable 42-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces 44A10 Laplace transform 46F05 Topological linear spaces of test functions, distributions and ultradistributions Keywords:Hilbert space; functions of a complex variable; Fourier and Laplace transforms; distributions Citations:Zbl 0459.46001; Zbl 1019.46001 PDFBibTeX XMLCite \textit{G. Cicogna}, Metodi matematici della fisica (Italian). Berlin: Springer (2008; Zbl 1157.00008)