This book is motivated by surface-surface intersection problems (SSI) in R3, self-intersection surfaces problem in R3 and three hypersurfaces intersection problems (SSSI) in R⁴. It presents algorithms for computing all the differential geometry properties of Frenet apparatus (t, n, b,κ,τ) of intersection curves of surfaces in R3 for transversal and tangential intersection. The surfaces may be implicit parameterization or parametric parameterization. It is also presents algorithms for computing all the differential geometry properties of intersection curves of Frenet apparatus...