Euler angles are a representation of an angular frame, as are quaternions and rotation matrices.
Euler angles are a set of three angles, corresponding to pitch, roll, and yaw. Euler angles may be constructed according to many conventions. The axes of and ordering of ordering of pitch, roll, and yaw vary by convention.
Euler angles are not commutative. For any Euler angles A, B, a rotation A followed by B is not
(B + A) is necessarily equal a rotation B followed by A (B + A). Because of this algebraic property, Euler angles are often not very useful for signal processing applications.
Euler angles suffer from a pair of singularity points at which only two of the three angles are significant. The derivative of the Euler angles is discontinuous at this point. This condition is often called gimbal lock.