The book "Local Cohomology: An Algebraic Introduction with Geometric Applications" by M. P. Brodmann and R. Y. Sharp provides a comprehensive introduction to local cohomology, a fundamental concept in commutative algebra and algebraic geometry. The authors define and explore the properties of local cohomology functors, torsion modules, and ideal transforms, providing a detailed treatment of the Mayer-Vietoris sequence, change of rings, and other advanced topics. The book also delves into fundamental vanishing theorems, graded versions of basic theorems, and applications to projective varieties and sheaf cohomology. Key results include the Lichtenbaum-Hartshorne theorem, Castelnuovo regularity, and bounds of diagonal type. The authors use both theoretical proofs and geometric interpretations to illustrate the concepts, making the book suitable for graduate students and researchers in algebraic geometry and commutative algebra.The book "Local Cohomology: An Algebraic Introduction with Geometric Applications" by M. P. Brodmann and R. Y. Sharp provides a comprehensive introduction to local cohomology, a fundamental concept in commutative algebra and algebraic geometry. The authors define and explore the properties of local cohomology functors, torsion modules, and ideal transforms, providing a detailed treatment of the Mayer-Vietoris sequence, change of rings, and other advanced topics. The book also delves into fundamental vanishing theorems, graded versions of basic theorems, and applications to projective varieties and sheaf cohomology. Key results include the Lichtenbaum-Hartshorne theorem, Castelnuovo regularity, and bounds of diagonal type. The authors use both theoretical proofs and geometric interpretations to illustrate the concepts, making the book suitable for graduate students and researchers in algebraic geometry and commutative algebra.