Basic real analysis

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Basic Real Analysis and Advanced Real Analysis systematically develop essential concepts and tools in real analysis crucial for all mathematicians, whether aspiring or established. These works offer a comprehensive treatment with a global perspective, highlighting the connections between real analysis and various mathematical branches. The development progresses from specific examples to general theories, often introducing practical applications before formal theory. The texts integrate real analysis with topics in algebra, topology, complex analysis, probability, differential geometry, and various applied mathematics fields. They feature numerous examples and hundreds of problems, with extensive sections providing hints or complete solutions for most. Aimed at young mathematicians, these books serve as excellent course texts and self-study resources, particularly for graduate students preparing for qualifying exams. Their scope and approach are appealing to instructors and professors across pure mathematics and to applied mathematicians in analytic fields such as statistics, mathematical physics, and differential equations. The clarity and breadth of these works make them a valuable addition to any mathematician's personal library.