This book aims to provide an account of recent developments in the theory of the Plateau problem on the surfaces and surfaces of the minimum H-surfaces and its analytical framework. An overview of classical theory and traditional theory of minimal surfaces and surfaces is presented, and recent developments are being explored into general structure theories of multiple solutions in full detail.

The book focuses on the derivation of Morse's inequality and in particular in passing the mountain pass from Morse Tompkins and Schiffmann to the minimal surfaces, evidence of large (unstable) H surfaces (Rellich's guess) because of Corazon Prezis, Stephen, and the author. Many related results are covered as well.

More than the engineering aspects of the Plato problem (which have been comprehensively covered elsewhere), the author emphasizes the analytical side. The focus is on the changing approach.

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