This thesis presents a modern approach to two Integral Boundary Layer methods implemented in the Python programming language. This work is based on two 2D boundary layer methods: Thwaites' method for laminar boundary layer flows and Head's method for turbulent boundary layer flows. Several novel enhancements improve the quality and usability of the results. These improvements include: a common ordinary differential equation (ODE) integration framework that generalizes computational implementations of Integral Boundary Layer methods; the use of a dense output Runge-Kutta ODE solver that allows for querying of simulation results at any point with accuracy to the same order as that of the solver; and an edge velocity treatment method using cubic spline interpolation that improves the simulation performance using only points from an inviscid edge velocity distribution. Both the laminar and turbulent methods are shown to benefit from smoothing of the edge velocity distribution. The choice of ODE solver alleviates the need to artificially limit step sizes. Comparisons against analytic solutions, experimental data and XFOIL results provide a wide varity of verification and validation cases with which to compare. The implementation of Thwaites' method in this thesis avoids simplifications made in other implementations of this method, which results in more robust results. The implementation of Head's method produces high-quality results typically found in other implementations while utilizing the common ODE integration framework. Utilizing the common ODE framework results in significantly less code needed to implement Thwaites' and Head's methods. In addition, the boundary layer solvers produce results in seconds for all results presented here. Boundary layer transition and separation criteria are implemented as a proof of concept, but require future work.