Basic Analysis I & II

Introduction to real analysis, from the real numbers, limits and continuity to metric spaces, multivariable differentiation and integration, and approximation. The book includes proofs, examples and exercises.

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By Jiří Lebl. Version 6.3, volumes I and II. This edition uses CC BY-SA 4.0; the author also offers CC BY-NC-SA 4.0. See the original licence notice.

Study in the programme

Volume I: real numbers, sequences, continuity, derivatives and the Riemann integral

Volume II: metric spaces, multivariable analysis and approximation

C10 — Real Analysis I · C20 — Real Analysis II

Author’s website · Versioned original LaTeX · Attribution and sources

HTML navigation and presentation adapted with OpenAI Codex — GPT-6 Astra, Ultra effort, and GPT-6.1 Sol, Ultra effort. The mathematical text is Jiří Lebl’s work.