YETI is a library offering an implementation of IsoGeometric Analysis based on NURBS and B-Splines. It is published under the GNU Lesser General Public Licence and comes in the form of a Python library allowing the user to enter the input data of a NURBS arametrization (as a text file inspired from Abaqus input files syntax). Stiffness and mass matrices and right hand side vector are computed to form linear systems for solving mechanical or thermal problems. Solid or Kirchhoff-Love shell elements are available. In the context of shape optimization, a NURBS parametrization can be set up with design variables based on control points position. YETI can compute the analytical sensitivities [1] of several quantities of interest (discrete compliance, volume, eigenvalues, displacement at given location, ...) that can be used in a gradient-based algorithm. For complex geometries involving multiple patches with non-conforming interfaces, a weak coupling strategy for the kinematic degrees of freedom, using a Mortar approach, is proposed. This latter is particularly suitable for a domain decomposition resolution, using a FETI (Finite Element Tiering and Interconnecting) algorithm [2]. To complete this coupling strategy in the field of shape optimization, an embedded approach [3] is set up to guarantee the geometric connection between a main patch to be optimized and adjacent patches representing geometric features as stiffeners or fillets. These patches are nested in a free form deformation hull controlled by the main patch shape change. Efficient solving of Partial Derivative Equations can be an issue for high degree B-Spline parametrization. An implementation of Matrix Free Weighted Quadrature [4] is proposed in YETI for transient thermal problems and is being extended to mechanical problems with non linear material behavior.