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This volume develops the structural theory of one-parameter semigroups of positive operators on ordered Banach spaces, addressing the fundamental problem of characterizing their generators, spectral properties, and asymptotic behavior. Such semigroups form a central analytical framework for models arising in partial differential equations, probability theory, ergodic theory, and mathematical physics.

Since its first publication in 1986, the book has become a foundational reference, offering a rigorous and unified treatment of positivity, Banach lattices, and semigroup theory. The exposition covers Banach spaces, Banach lattices, C(X) spaces, and operator algebras, with a systematic focus on generator theory, spectral analysis, and long-time behavior.

This second edition preserves the original conceptual framework and organization while presenting the entire text in a fully revised and professionally typeset form. Misprints have been corrected, references updated, and a new chapter of notes surveys key developments of the past four decades, placing the original results in a modern context without compromising their historical coherence. The book remains an essential resource for researchers and advanced graduate students in operator theory and functional analysis.