Presenting a thorough introductory exposition of optimal control theory, this work differs from the existing textbooks on the subject due to its emphasis on the economic interpretation of the mathematics and the qualitative properties of the solutions. Moreover, it is a modern exposition of optimal control theory in that it presents numerous complementary methods. It is aimed at first-year and second-year PhD students in economics, agricultural and resource economics, operations research, management science, and applied mathematics.

1. Essential elements of continuous time dynamic optimization 2. Necessary conditions for a simplified control problem 3. Concavity and sufficiency in optimal control problems 4. The maximum principle and economic interpretations 5. Linear optimal control problems 6. Necessary and sufficient conditions for a general class of control problems 7. Necessary and sufficient conditions for isoperimetric problems 8. Economic characterization of reciprocal isoperimetric problems 9. The dynamic envelope theorem and economic interpretations 10. The dynamic envelope theorem and transversality conditions 11. Comparative dynamics via envelope methods 12. Discounting, current values, and time consistency 13. Local stability and phase portraits of autonomous differential equations 14. Necessary and sufficient conditions for infinite horizon control problems 15. The neoclassical optimal economic growth model 16. A dynamic limit pricing model of the firm 17. The adjustment cost model of the firm 18. Qualitative properties of infinite horizon optimal control problems with one state variable and one control variable 19. Dynamic programming and the Hamilton-Jacobi-Bellman equation 20. Intertemporal duality in the adjustment cost model of the firm.

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