This thesis treats some of the problems related to the good drawings D$ sb{ rm n}$ of the complete graph K$ sb{ rm n}$. The first of these problems is obtaining all the non-isomorphic good drawings D$ sb{ rm n}$ of K$ sb{ rm n}$. After conjecturing that any good drawing D$ sb{ rm n}$ of K$ sb{ rm n}$ has at least one crossing-free Hamiltonian Circuit, an algorithm generating all the non-isomorphic good drawings D$ sb{ rm n}$ of K$ sb{ rm n}$ is developed. The second problem, determining the existence of a rectilinear drawing D$ sb{ rm n}$ of K$ sb{ rm n}$ with a given set of crossings, is solved by finding a characteristic of the rectilinear drawings D$ sb{ rm n}$ of K$ sb{ rm n}$. An algorithm using this characteristic determines whether a given set of crossing defines a rectilinear drawing D$ sb{ rm n}$ of K$ sb{ rm n}$. The last problem, to generate all the non-isomorphic rectilinear drawings D$ sb{ rm n}$ of K$ sb{ rm n}$, is solved by an algorithm using a set of rectilinear drawings D$ sb{ rm n-1}$ of K$ sb{ rm n-1}$.

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