1. Models Computability and Numberings. - 1. 1. Algebraic Systems Models and Theories. - 1. 2. Notions and Definitions of Algorithm Theory. - 1. 3. The Main Notions and Results of Numbering Theory. - 1. 4. Numbered Algebraic Systems. - 2. Constructive Models. - 2. 1. The Simplest Properties. - 2. 2. Existence of Constructivizations. - 2. 3. The Kernel Theorem and Applications. - 2. 4. Theories with Finite Obstacles. - 2. 5. Constructive Fields. - 3. Strongly Constructive and Decidable Models. - 3. 1. Strong Constructivizability and Types. - 3. 2. Effective Extensions. - 3. 3. Decidability of Homogeneous Models. - 4. Theories with a Countable Set of Countable Models. - 4. 1. Theories with Decidable Models. - 4. 2. The Ehrenfeucht Theories. - 4. 3. The Complexity of Countable Models of Ehrenfeucht Theories. - 5. Algorithmic Dimensions and Computable Classes. - 5. 1. Infinite Algorithmic Dimensions. Criteria. - 5. 2. Computability and Effectively Infinite Classes. - 6. Models of Finite Algorithmic Dimension and Autostability. - 6. 1. Autostable Models. - 6. 2. Algebraic Systems of Finite Algorithmic Dimension. - References. Language: English