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I: Theory.- I. Stochastic processes in general.- 1. Basic definitions.- 2. Markov processes, transition functions, resolvents, and generators.- 3. Feller processes, Feller-Dynkin processes, and the strong Markov property.- 4. Martingales.- II. Linear diffusions.- 1. Basic facts.- 2. Local time.- 3. Passage times.- 4. Additive functionals and killing.- 5. Excessive functions.- 6. Ergodic results.- III. Stochastic calculus.- 1. Stochastic integration with respect to Brownian motion.- 2. The Itô and Tanaka formulae.- 3. The Cameron-Martin-Girsanov transformation of measure.- 4. Stochastic differential equations - strong solutions.- 5. Stochastic differential equations - weak solutions.- 6. One-dimensional stochastic differential equations.- IV. Brownian motion.- 1. Definition and basic properties.- 2. Brownian local time.- 3. Excursions.- 4. Brownian bridge.- 5. Brownian motion with drift.- 6. Bessel processes.- V. Local time as a Markov process.- 1. Diffusion local time.- 2. Local time of Brownian motion.- 2. Local time of Brownian motion with drift.- 4. Local time of Bessel process.- VI. Differential systems associated to Brownian motion.- 1. The Feynman-Kac formula.- 2. Exponential stopping.- 3. Stopping at first exit time.- 4. Stopping at inverse additive functional.- Appendix 1. Briefly on some diffusions.- II: Tables of Distributions of Functionals of Brownian Motion and Related Processes.- 1. Brownian motion.- 1. Exponential stopping.- 2. Stopping at first hitting time.- 3. Stopping at first exit time.- 4. Stopping at inverse local time.- 2. Brownian motion with drift.- 1. Exponential stopping.- 2. Stopping at first hitting time.- 3. Stopping at first exit time.- 4. Stopping at inverse local time.- 3. Reflecting Brownian motion.- 1. Exponential stopping.- 2. Stopping at first hitting time.- 4. Stopping at inverse local time.- 4. Bessel process of order zero.- 1. Exponential stopping.- 2. Stopping at first hitting time.- 3. Stopping at first exit time.- 4. Stoppi