I. Sums of a Random Number of Random Variables. - 1. 1. Sampling sums of dependent variables and mixtures of infinitely divisible distributions. - 1. 2. Limit theorems for a sum of randomly indexed sequences. - 1. 3. Necessary and sufficient conditions and limit theorems for sampling sums. - II. Branching Processes with Generalized Immigration. - 2. 1. Classical models of branching processes. - 2. 2 General branching processes with reproduction dependent immigration. - 2. 3. Discrete time processes. - 2. 4. Convergence to Jirina processes and transfer theorems for branching processes. - III. Branching Processes with Time-Dependent Immigration. - 3. 1. Decreasing immigration. - 3. 2. Increasing immigration. - 3. 3. Local limit theorems. - IV. The Asymptotic Behavior of Families of Particles in Branching Processes. - 4. 1. Sums of dependent indicators. - 4. 2. Family of particles in critical processes. - 4. 3. Families of particles in supercritical and subcritical processes. - References. Language: English