This chapter discusses scattering resonance phenomena, focusing on Feshbach resonances in ultracold gases. It begins by introducing the concept of resonances in quantum scattering, highlighting their connection to bound states and virtual states. The chapter then delves into the specific types of resonances, including shape resonances, potential resonances, and Feshbach resonances, each with distinct characteristics and applications. Shape resonances arise from long-lived states within potential barriers, while potential resonances occur in the absence of barriers and are characterized by scattering lengths. Feshbach resonances, on the other hand, involve multiple collision channels and are crucial for tuning the scattering length via external magnetic fields. The chapter derives the dependence of the scattering phase shift on magnetic field and collision energy, leading to expressions for the scattering length and effective range coefficient, which are particularly useful for ultracold gases. The chapter also covers the underlying atom-atom interactions, including hyperfine and Zeeman energies, and the coupled-channels radial Schrödinger equation. It introduces the projection operator formalism for Feshbach resonances, which allows for the analytic expression of the scattering matrix. The treatment includes both open and closed channel scattering, with a focus on the energy-dependent scattering phase shift, scattering length, and effective range coefficient. Finally, the chapter discusses the ultracold limit, where the two-body potential is negligible, and the asymptotic radial wave functions are derived. It provides detailed expressions for the scattering phase shift, scattering length, and effective range coefficient in the presence of potential resonances and Feshbach resonances, including resonant open channel interactions. The chapter concludes with a discussion on the practical applications of Feshbach resonances in ultracold gases, such as tuning the scattering length and exploring the BCS-BEC crossover.This chapter discusses scattering resonance phenomena, focusing on Feshbach resonances in ultracold gases. It begins by introducing the concept of resonances in quantum scattering, highlighting their connection to bound states and virtual states. The chapter then delves into the specific types of resonances, including shape resonances, potential resonances, and Feshbach resonances, each with distinct characteristics and applications. Shape resonances arise from long-lived states within potential barriers, while potential resonances occur in the absence of barriers and are characterized by scattering lengths. Feshbach resonances, on the other hand, involve multiple collision channels and are crucial for tuning the scattering length via external magnetic fields. The chapter derives the dependence of the scattering phase shift on magnetic field and collision energy, leading to expressions for the scattering length and effective range coefficient, which are particularly useful for ultracold gases. The chapter also covers the underlying atom-atom interactions, including hyperfine and Zeeman energies, and the coupled-channels radial Schrödinger equation. It introduces the projection operator formalism for Feshbach resonances, which allows for the analytic expression of the scattering matrix. The treatment includes both open and closed channel scattering, with a focus on the energy-dependent scattering phase shift, scattering length, and effective range coefficient. Finally, the chapter discusses the ultracold limit, where the two-body potential is negligible, and the asymptotic radial wave functions are derived. It provides detailed expressions for the scattering phase shift, scattering length, and effective range coefficient in the presence of potential resonances and Feshbach resonances, including resonant open channel interactions. The chapter concludes with a discussion on the practical applications of Feshbach resonances in ultracold gases, such as tuning the scattering length and exploring the BCS-BEC crossover.