This report provides a comprehensive overview of the Askey-scheme of hypergeometric orthogonal polynomials and their $q$-analogues. The Askey-scheme categorizes these polynomials based on their orthogonality properties, recurrence relations, and generating functions. The report is structured into several chapters: 1. **Hypergeometric Orthogonal Polynomials**: This chapter defines the classical hypergeometric orthogonal polynomials, including Wilson, Racah, continuous dual Hahn, continuous Hahn, Hahn, dual Hahn, Meixner-Pollaczek, Jacobi, Gegenbauer/Ultraspherical, Chebyshev, Legendre/Spherical, Meixner, Krawtchouk, Laguerre, Charlier, and Hermite polynomials. It covers their orthogonality relations, three-term recurrence relations, and generating functions. 2. **Limit Relations**: This chapter discusses the limit relations between different classes of orthogonal polynomials within the Askey-scheme, providing a detailed list of transitions between various families. 3. **$q$-Analogue of Hypergeometric Orthogonal Polynomials**: This chapter introduces the $q$-analogue of the polynomials in the Askey-scheme, including Askey-Wilson, q-Racah, continuous dual q-Hahn, continuous q-Hahn, big q-Jacobi, q-Hahn, dual q-Hahn, Al-Salam-Chihara, q-Meixner-Pollaczek, continuous q-Jacobi, big q-Laguerre, little q-Jacobi, q-Meixner, quantum q-Krawtchouk, q-Krawtchouk, affine q-Krawtchouk, dual q-Krawtchouk, continuous big q-Hermite, continuous q-Laguerre, little q-Laguerre/Wall, q-Laguerre, alternative q-Charlier, q-Charlier, Al-Salam-Carlitz I, Al-Salam-Carlitz II, continuous q-Hermite, Stieltjes-Wigert, discrete q-Hermite I, and discrete q-Hermite II polynomials. It provides their definitions, orthogonality relations, three-term recurrence relations, and generating functions. 4. **Limit Relations Between $q$-Analogue Polynomials**: This chapter details the limit relations between the basic hypergeometric orthogonal polynomials, showing how different families can transform into each other. 5. **From Classical to $q$-Analogue**: This chapter explains how the classical hypergeometric orthogonal polynomials can be derived from their $q$-analogue, providing a bridge between the two families. The report also includes a bibliography and index, and acknowledges the contributions of Professor Tom H. Koornwinder, who suggested the project and provided valuable assistance. The authors aim toThis report provides a comprehensive overview of the Askey-scheme of hypergeometric orthogonal polynomials and their $q$-analogues. The Askey-scheme categorizes these polynomials based on their orthogonality properties, recurrence relations, and generating functions. The report is structured into several chapters: 1. **Hypergeometric Orthogonal Polynomials**: This chapter defines the classical hypergeometric orthogonal polynomials, including Wilson, Racah, continuous dual Hahn, continuous Hahn, Hahn, dual Hahn, Meixner-Pollaczek, Jacobi, Gegenbauer/Ultraspherical, Chebyshev, Legendre/Spherical, Meixner, Krawtchouk, Laguerre, Charlier, and Hermite polynomials. It covers their orthogonality relations, three-term recurrence relations, and generating functions. 2. **Limit Relations**: This chapter discusses the limit relations between different classes of orthogonal polynomials within the Askey-scheme, providing a detailed list of transitions between various families. 3. **$q$-Analogue of Hypergeometric Orthogonal Polynomials**: This chapter introduces the $q$-analogue of the polynomials in the Askey-scheme, including Askey-Wilson, q-Racah, continuous dual q-Hahn, continuous q-Hahn, big q-Jacobi, q-Hahn, dual q-Hahn, Al-Salam-Chihara, q-Meixner-Pollaczek, continuous q-Jacobi, big q-Laguerre, little q-Jacobi, q-Meixner, quantum q-Krawtchouk, q-Krawtchouk, affine q-Krawtchouk, dual q-Krawtchouk, continuous big q-Hermite, continuous q-Laguerre, little q-Laguerre/Wall, q-Laguerre, alternative q-Charlier, q-Charlier, Al-Salam-Carlitz I, Al-Salam-Carlitz II, continuous q-Hermite, Stieltjes-Wigert, discrete q-Hermite I, and discrete q-Hermite II polynomials. It provides their definitions, orthogonality relations, three-term recurrence relations, and generating functions. 4. **Limit Relations Between $q$-Analogue Polynomials**: This chapter details the limit relations between the basic hypergeometric orthogonal polynomials, showing how different families can transform into each other. 5. **From Classical to $q$-Analogue**: This chapter explains how the classical hypergeometric orthogonal polynomials can be derived from their $q$-analogue, providing a bridge between the two families. The report also includes a bibliography and index, and acknowledges the contributions of Professor Tom H. Koornwinder, who suggested the project and provided valuable assistance. The authors aim to