Some coloring problems in Ramsey theory

In this thesis, we present new results which are concerned with the following four coloring problems in Ramsey Theory. \begin{enumerate}\item[i.] The finite form of Brown's Lemma.\item[ii.] Some 2-color Rado numbers.\item[iii.] Ramsey results involving Fibonacci sequences.\item[iv.] Coloring the odd-distance plane graph.\end{enumerate} A few of the results in this thesis are cited from earlier works of other authors. Several results are cited from papers co-authored by the present author. All other results are new.