Master the intricacies of real analysis with "Real Analysis and Applications" by Fabio Silva Botelho. This comprehensive textbook offers a rigorous yet accessible introduction to one and n-dimensional real analysis, perfect for undergraduate and beginning graduate students. Part I delves into fundamental concepts like the construction of real numbers, metric spaces, and sequences and series. Part II expands upon these foundations to explore multi-variable real analysis, featuring detailed proofs of the implicit theorem for the vectorial case and an introduction to Riemannian geometry. Key Features: * Covers real analysis in one and n dimensions. * Rigorous and elegant proofs for deeper understanding. * Suitable for undergraduate and graduate students. * Explores advanced topics including differential forms and Riemannian geometry. This self-contained work provides a well-founded, detailed approach to real analysis and its applications, making it an invaluable resource for students and researchers alike. Summary: Real Analysis and Applications, Hardcover, English, 567 pages, First edition, ISBN 9783319786308, published by Springer Cham, written by Fabio Silva Botelho.