Introduction and statement of results Glossary of notation and conventions Gorenstein del Pezzo surfaces Bug-eyed covers Log deformation theory Criteria for log uniruledness Reduction to $\pi^{\text{alg}}_{1}(S^0)=\{1\}$ Flushness and preparation for the hunt Bogomolov bound Riemann Roch and surfaces with small coefficient A partial classification of $K_{T}$-contractions the linear system $\vert K_{S} + A\vert$ Classification of bananas and fences $T_1$ a net $g(A_1)>1$ $A_1$ has a simple cusp $A_1$ has a simple node $A_1$ smooth The smooth banana Proof of (1.1) and corollaries A surface with $\pi^{\text{alg}}_1(S^0)=\{1\}$ but no tiger Tigers, complements and toric pairs Classification of almost all rank one log del Pezzos Appendix: Log terminal surface singularities and adjunction Appendix: Normalisation of an algebraic space Index to obscure or unconventional notation References.
