I. Linear Models.- 1. The Poisson Process.- 2. Birth and Death Processes.- 2.1 Linear Birth Process.- 2.2 Linear Birth and Death Process.- 2.3 Birth and Death with Carrying Capacity.- 3. Branching Processes.- 3.1 Continuous Time.- 3.2 Galton-Watson Process.- II. Epidemics.- 1. Reed-Frost Model.- 1.1 Deterministic Version.- 1.2 Two Methods for the Study of the Reed-Frost Model.- 1.3 Backward Equation.- 2. Qualitative Theory for the General Stochastic Epidemic.- 2.1 Approximation by Birth and Death Process.- 2.2 Deterministic Theory (Kermack and McKendrick).- 2.3 Diffusion Approximation.- 2.4 Practice Problem.- 2.5 Gaussian Approximation for General Diffusion Equations.- III. Diffusion Equations.- 1. Introduction.- 2. Derivation of the Forward and Backward Equation.- 3. Random Genetic Drift.- 4. Solutions which are Valid for Small Time.- 5. Random Drift and Selection.- 6. Wright' s Formula for Equilibrium Distributions.- IV. Dynamical Systems Perturbed by Noise.- 1. One Species.- 2. Several Species-Gradient Fields.- 3. Ray Method for General Systems.