This chapter discusses Feshbach resonances in ultracold gases, focusing on the mechanism of scattering resonances that require a multi-channel treatment. It describes how the scattering phase shift depends on magnetic field and collision energy, and how the scattering length and effective range coefficient can be extracted from this. These parameters are particularly useful for ultracold gases. Resonances in quantum scattering often arise from nearby bound states, which can be long-lived or virtual. A shape resonance occurs within a potential barrier, typically a centrifugal barrier due to non-zero angular momentum. The collision energy controls the cross section, and the scattering phase shift changes rapidly across a resonance energy interval. The Breit-Wigner formula describes the cross section for these resonances. A potential resonance occurs in the absence of a barrier and is a s-wave phenomenon. It is characterized by a large scattering length, which is much larger than the interaction potential range. In ultracold gases, the s-wave scattering length is crucial for characterizing binary interactions. Feshbach resonances involve multiple collision channels and differ from single-channel resonances. They occur due to interference between background scattering processes in an open channel and resonant scattering in a closed channel. This allows a closed-channel bound state to transform into a long-lived resonant state. Feshbach resonances are important for tuning the scattering length via external magnetic fields, enabling control over interactions in ultracold gases. The scattering length is given by a formula that depends on the background scattering length, the resonance field, and the field range. Feshbach resonances were first described in nuclear physics and later applied to quantum gases. They allow for tuning the sign and strength of interatomic interactions, which is essential for studying phenomena like the BCS-BEC crossover. The chapter also discusses the Fano resonance, which is similar to a Feshbach resonance but is characterized by an asymmetric cross-section. Both resonances share the same origin: interference between background and resonant scattering processes. The chapter provides a detailed treatment of Feshbach resonances, starting with the underlying interatomic interactions, followed by the concept of multi-channel scattering and the coupled-channels radial Schrödinger equation. It then describes the projection operator formalism for Feshbach resonances, leading to expressions for the scattering matrix that include physical parameters like the background scattering length, resonance width, and position. The treatment includes the introduction of an additional bound or virtual state in the open channel to account for resonant open channel interactions. The chapter concludes with the derivation of expressions for different types of resonances relevant to ultracold scattering, such as the energy-dependent scattering phase shift, scattering length, and effective range coefficient.This chapter discusses Feshbach resonances in ultracold gases, focusing on the mechanism of scattering resonances that require a multi-channel treatment. It describes how the scattering phase shift depends on magnetic field and collision energy, and how the scattering length and effective range coefficient can be extracted from this. These parameters are particularly useful for ultracold gases. Resonances in quantum scattering often arise from nearby bound states, which can be long-lived or virtual. A shape resonance occurs within a potential barrier, typically a centrifugal barrier due to non-zero angular momentum. The collision energy controls the cross section, and the scattering phase shift changes rapidly across a resonance energy interval. The Breit-Wigner formula describes the cross section for these resonances. A potential resonance occurs in the absence of a barrier and is a s-wave phenomenon. It is characterized by a large scattering length, which is much larger than the interaction potential range. In ultracold gases, the s-wave scattering length is crucial for characterizing binary interactions. Feshbach resonances involve multiple collision channels and differ from single-channel resonances. They occur due to interference between background scattering processes in an open channel and resonant scattering in a closed channel. This allows a closed-channel bound state to transform into a long-lived resonant state. Feshbach resonances are important for tuning the scattering length via external magnetic fields, enabling control over interactions in ultracold gases. The scattering length is given by a formula that depends on the background scattering length, the resonance field, and the field range. Feshbach resonances were first described in nuclear physics and later applied to quantum gases. They allow for tuning the sign and strength of interatomic interactions, which is essential for studying phenomena like the BCS-BEC crossover. The chapter also discusses the Fano resonance, which is similar to a Feshbach resonance but is characterized by an asymmetric cross-section. Both resonances share the same origin: interference between background and resonant scattering processes. The chapter provides a detailed treatment of Feshbach resonances, starting with the underlying interatomic interactions, followed by the concept of multi-channel scattering and the coupled-channels radial Schrödinger equation. It then describes the projection operator formalism for Feshbach resonances, leading to expressions for the scattering matrix that include physical parameters like the background scattering length, resonance width, and position. The treatment includes the introduction of an additional bound or virtual state in the open channel to account for resonant open channel interactions. The chapter concludes with the derivation of expressions for different types of resonances relevant to ultracold scattering, such as the energy-dependent scattering phase shift, scattering length, and effective range coefficient.