Isogeometric analysis is a method that integrates CAD geometry with finite element analysis, using NURBS (Non-Uniform Rational B-Splines) to represent geometry exactly. This approach allows for geometrically exact models without the need for meshing, and enables efficient refinement through h-, p-, and k-refinement. The method is particularly effective for problems involving thin shells, fluid dynamics, and structural mechanics, where maintaining exact geometry is crucial. The basis functions used in isogeometric analysis are complete with respect to affine transformations, ensuring accurate representation of rigid body motions and constant strain states. Numerical examples demonstrate optimal convergence rates for linear elasticity problems and convergence to thin elastic shell solutions. The k-refinement strategy is shown to converge toward monotone solutions for advection-diffusion processes with sharp internal and boundary layers. Isogeometric analysis is argued to be a viable alternative to traditional finite element analysis, offering advantages in accuracy, efficiency, and robustness. The method is based on NURBS, which are widely used in CAD systems, and allows for seamless integration with CAD geometry. The approach involves constructing meshes from NURBS surfaces, enabling adaptive refinement without communication with CAD systems. The method has been applied to various problems, including the analysis of infinite plates with circular holes, thick cylinders under internal pressure, and solid horseshoes under in-plane displacements. The results demonstrate the effectiveness of isogeometric analysis in achieving accurate and efficient solutions for complex engineering problems.Isogeometric analysis is a method that integrates CAD geometry with finite element analysis, using NURBS (Non-Uniform Rational B-Splines) to represent geometry exactly. This approach allows for geometrically exact models without the need for meshing, and enables efficient refinement through h-, p-, and k-refinement. The method is particularly effective for problems involving thin shells, fluid dynamics, and structural mechanics, where maintaining exact geometry is crucial. The basis functions used in isogeometric analysis are complete with respect to affine transformations, ensuring accurate representation of rigid body motions and constant strain states. Numerical examples demonstrate optimal convergence rates for linear elasticity problems and convergence to thin elastic shell solutions. The k-refinement strategy is shown to converge toward monotone solutions for advection-diffusion processes with sharp internal and boundary layers. Isogeometric analysis is argued to be a viable alternative to traditional finite element analysis, offering advantages in accuracy, efficiency, and robustness. The method is based on NURBS, which are widely used in CAD systems, and allows for seamless integration with CAD geometry. The approach involves constructing meshes from NURBS surfaces, enabling adaptive refinement without communication with CAD systems. The method has been applied to various problems, including the analysis of infinite plates with circular holes, thick cylinders under internal pressure, and solid horseshoes under in-plane displacements. The results demonstrate the effectiveness of isogeometric analysis in achieving accurate and efficient solutions for complex engineering problems.