I Dynamic Models of Resource Extraction in Markets of Monopoly or Pure Competition with Full Information -- 1. Hotelling’s Model -- 2. Optimal Extraction Rates and Exploration -- 2.1 Pure Competition -- 2.2 Monopoly -- 3. Optimal Extraction Rates and Constant Elasticity of Demand -- 4. Market Structure and Optimal Depletion Rates -- 4.1 Pure Competition -- 4.2 Monopoly -- 5. Extraction of an Exhaustible Resource and Production of a Substitute -- 5.1 Social Optimum -- 5.2 Extraction of the Resource and Production of the Substitute by the same Monopoly -- 5.3 Many Owners of the Resource and Production of the Substitute by Monopoly -- 5.4 Many Owners of the Resource and Production of the Substitute by all -- 6. Extraction of Durable Exhaustible Resources -- 6.1 Discrete Time -- 6.2 Continuous Time -- 6.2.1 Pure Competition -- 6.2.2 Monopoly -- 7. Conclusions -- II Dynamic Models with Uncertainty and Monopolistic Markets or Pure Competition -- 1. Optimal Extraction Rates and Uncertainty with Respect to R&D towards Future Technologies -- 1.1 Exogenous Technical Progress -- 1.1.1 Basic Model -- 1.1.2 First Extension: Production -- 1.1.3 Second Extension: Exhaustible Resources -- 1.1.4 Third Extension: Uncertainty about the Future Technological Development -- 1.2 Endogenous Technical Progress -- 1.2.1 Basic Model -- 1.2.2 Modification of the Basic Model -- 1.2.3 Example with Exponentially Distributed Z -- 2. Optimal Extraction Rates and Unknown Reserves -- 2.1 Monopolistic Extraction Rates Depending on Time only -- 2.2 Monopolistic Extraction Rates Depending on Time and Quantities already Extracted -- 2.3 Optimal Extraction Rates and Pure Competition -- 2.3.1 Basic Model -- 2.3.2 Example with Two Suppliers -- 2.4 Optimal Extraction Rates from Consumer’s View -- 2.4.1 Basic Model -- 2.4.2 Example with Exponentially Distributed Z -- 2.5 Pure Competition and Optimal Extraction -- 3. Optimal Extraction Rates and Unknown Costs of the Development of a Substitute -- 3.1 One-period Analysis and Monopoly -- 3.2 One-period Analysis and Pure Competition -- 3.3 Two-period Analysis -- 3.3.1 Optimal Extraction and One Decision Maker -- 3.3.1.1 Basic Model -- 3.3.1.2 Example with Linear Demand -- 3.3.2 Optimal Extraction and Pure Competition -- 3.3.3 Extraction of the Resource and Production of the Substitute by Exactly One Monopoly -- 4. Conclusions -- III Short Introduction to the Theory of Differential Games -- IV Dynamic Models of Resource Extraction and Duopolistic Markets -- 1. An Introductory Duopoly Model with Production Strategies -- 2. Duopoly with Price Strategies and Exploration -- 2.1 Open-loop Controls -- 2.2 Closed-loop Controls -- 3. A Duopoly Model with Quantity Strategies -- 3.1 Introduction of the Model -- 3.2 Specialization of the Model: Linear-Quadratic Differential Game -- 4. Cartelization and Optimal Extraction of Exhaustible Resources -- 4.1 Pure Competition -- 4.2 Monopolistic Behaviour of the Cartel -- 4.3 Implications of Cartelization to the Profits of the Non-Cartel -- 5. Oligopoly with Discrete Time Parameter -- 6. Conclusions -- V Oligopolistic Extraction with Continuous Time -- 1. Basic Model with Quantity Strategies -- 1.1 Introduction of the Model -- 1.2 Algorithm for the Determination of a Nash Equilibrium -- 2. Specializations of the Basic Model -- 2.1 Fixed Resource Stock -- 2.2 Deterministic Expandable Resource Stocks -- 3. Oligopoly and Price Strategies -- 4. Conclusions.