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This thesis is concerned with the numerical solution of three integral equations of Volterra type. Chapter 1 presents some basic notation and mathematical results. Chapter 2 is concerned with linear multistep methods for the direct solution of Volterra integral equations of the first kind with a kernel identically equal to zero when t = s . A numerical method for solving a non-línear singular integral equation describing the temperature distribution of the surface of a projectile moving through a laminar boundary layer is discussed in Chapter 3. The convergence of this product integration method is given. Chapter4 generalises the previous chapter for a method of order n. Finally Chapter 5 treats a numerical method for a non-linear integral equation arising from non-linear waves in shock tubes.