A mathematician who has taken the romantic decision to devote himself to biology will doubtlessly look upon cell kinetics as the most simple and natural field of application for his knowledge and skills. Indeed, the thesaurus he is to master is not so complicated as, say, in molecular biology, the structural elements of the system, i. e. ceils, have been segregated by Nature itself, simple considerations of balance may be used for deducing basic equations, and numerous analogies in other areas of science also superficial add to one"s confidence. Generally speaking, this number of impression is correct, as evidenced by the very great theoretical studies on population kinetics, unmatched in other branches of mathematical biology. This, however, does not mean that mathematical theory of cell systems has traversed in its development a pathway free of difficulties or errors. The seeming ease of formalizing the phenomena of cell kinetics not infrequently led to the appearance of mathematical models lacking in adequacy or effectiveness from the viewpoint of applications. As in any other domain of science, mathematical theory of cell systems has its own intrinsic logic of development which, however, depends in large measure on the progress in experimental biology. Thus, during a fairly long period running into decades activities in that sphere were centered on devising its own specific approaches necessitated by new objectives in the experimental in vivo and in vitro investigation of cell population kinetics in different tissues.

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References.- I Some Points of the Theory of Branching Stochastic Processes.- 1.1. Introduction.- 1.2. The Galton-Watson Process.- 1.3. The Bellman-Harris Process.- 1.4. Asymptotic Behaviour of the Bellman-Harris Process Characteristics.- 1.5. The Multitype Age-Dependent Branching Processes.- References.- II Induced Cell Proliferation Kinetics within the Framework of a Branching Process Model.- 2.1. Introduction.- 2.2. The Subsequent Generations of Cells Induced to Proliferate.- 2.3. Age Distributions in Successive Generations.- 2.4. A Multitype Branching Process Model and Induced Cell Proliferation Kinetics.- 2.5. Grain Count Distribution and Branching Stochastic Processes.- References.- III Semistochastic Models of Cell Population Kinetics.- 3.1. Introduction.- 3.2. Integral Equations of Steady-State Dynamics of a Transitive Cell Population.- 3.3. Investigation of Periodic Processes in Cell Kinetics.- 3.4. Basic Integral Equations for Unsteady State Cell Kinetics.- 3.5. Construction of the q-index of the S-phase in a Special Case.- 3.6. Examples of Constructing Transient Processes for Particular States of Cell Kinetics.- 3.7. Analysis of the Process of Cell Blocking in the Mitotic Cycle.- References.- IV The Fraction Labelled Mitoses Curve in Different States of Cell Proliferation Kinetics.- 4.1. Introduction.- 4.2. "Flux-expectations" Concept and the Fraction Labelled Mitoses Curve.- 4.3. Mathematical Model Based on Transient Phenomena in Cell Kinetics.- 4.4. Investigation of Labelled Mitoses Curve Behaviour under Unsteady-State Cell Kinetics Conditions.- 4.5. Labelled Mitoses Curve under the Conditions of the Diurnal Rhythm of Cell Proliferation Processes.- References.- V Applications of Kinetic Analysis. Rat Liver Regeneration.- 5.1. Introduction.- 5.2. Kinetic Analysis of Induced Hepatocyte Proliferation in Regenerating Rat Liver.- 5.3. Dynamic Replacement of Hepatocytes, a Mechanism Maintaining Specialized Functions of the Regenerating Liver.- 5.4. A Simple Mathematical Model of Liver Response to Partial Hepatectomy of Different Extent.- References.- Conclusion.