Contents: Section-A: Ordinary Differential Equations. 1. Some basic concepts. 2. Solution of differential equations with first order and first degree. 3. Exact differential equations. 4. Bernoulli's linear and differential equations. 5. First order higher degree differential equations. 6. Singular solution and Clairaut's differential equations. 7. Orthogonal trajectories. 8. Homogeneous linear differential equations. 9. Non-homogeneous linear differential equations. 10. Method of variation of parameters and undetermined coefficients. 11. Equations reducible to linear differential equations with constant coefficients. 12. Simultaneous differential equations. 13. Solution of differential equations. 14. Legendre polynomials and Bessel functions. 15. Applications of ordinary differential equations. Section-B: Partial Differential Equations. 16. Introduction to partial differential equations. 17. Solution of linear partial differential equations of the first order. 18. Nonlinear partial differential equations of the first order. 19. General methods of solution of nonlinear partial differential equations of the first order. 20. Homogeneous linear partial differential equations with constant coefficients. 21. Non-homogeneous linear partial differential equations with constant coefficients. 22. Partial differential equations reducible to equations with constant coefficients. 23. Classification of linear partial differential equations of the second order. 24. Monge's methods. 25. Applications of partial differential equations. Section-C: Laplace Transforms, Fourier Transforms and Fourier Series. 26. Introduction to Laplace transforms. 27. Laplace transforms of derivatives and integrals. 28. First and second shifting theorems. 29. Differentiation and integration of Laplace transforms. 30. Convolution theorem and Laplace transform of periodic functions. 31. Solution of partial differential equations using Laplace transforms. 32. Introduction to Fourier series. 33. Fourier transforms. 34. Solution of differential equations using Fourier transforms. Bibliography. Index. Designed for undergraduate and postgraduate students of Mathematics this book can be used as an introductory book on Differential Equations for those working in the area of science and engineering and preparing for various competitive examinations. This book includes almost all the methods for finding solution of ordinary differential equations and partial differential equations with applications. The text also contains the topics of Laplace transforms and Fourier transforms and their applications in finding solutions of differential equations.