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I. Some Reminders of Functional Analysis.- II. Some Classes of Operators.- 1. Finite-Dimensional Operators.- 2. Bounded Linear Operators on a Banach Space.- 3. Bounded Linear Operator on a Hilbert Space.- III. Banach Algebras.- 1. Definition and Examples.- 2. Invertible Elements and Spectrum.- 3. Holomorphic Functional Calculus.- 4. Analytic Properties of the Spectrum.- IV. Representation Theory.- 1. Gelfand Theory for Commutative Banach Algebras.- 2. Representation Theory for Non-Commutative Banach Algebras.- V. Some Applications of Subharmonicity.- 1. Some Elementary Applications.- 2. Spectral Characterizations of Commutative Banach Algebras.- 3. Spectral Characterizations of the Radical.- 4. Spectral Characterizations of Finite-Dimensional Banach Algebras.- 5. Automatic Continuity for Banach Algebra Morphisms.- 6. Elements with Finite Spectrum.- 7. Inessential Elements.- VI. Representation of C?-algebras and the Spectral Theorem.- 1. Banach Algebras with Involution.- 2. C?-algebras.- 3. The Spectral Theorem.- 4. Applications.- VII. An Introduction to Analytic Multifunctions.- 1. Definitions and General Properties.- 2. The Oka-Nishino Theorem and Its Applications.- 3. Distribution of Values of Analytic Multifunctions.- 4. Conclusion.- 1. Subharmonic Functions and Capacity.- 2. Functions of Several Complex Variables.- References.- Author and Subject Index.