Additional errata (checked out): \item?p.27?, (Dwight Spencer) second line from bottom: T:S\to T should be $t:S\to T$. \item?p. 53? (Dwight Spencer) The display in the middle of the page should be: $i(T,LA)(L(f\o h)) = \eta A\o f\o h = RLf\o \eta D\o h = RLf\o i(T,LD)(Lh) = i(T,LA)(Lf\o Lh)$ In diagram (7), just below, the vertical arrows should be pointing upward. \item?p. 54? lines 5 from the bottom: (Dwight Spencer) change ``arrow for'' to ``element of the functor''. Add to the last sentence ``(A universal element of $\Hom(A,R(-))$ is called a {\bf universal arrow} for $R$ and $A$.)'' \item?p. 55? line 4: (Dwight Spencer) change $RLA$ to $RWA$. \item?p. 55? line 14: (Dwight Spencer) Change $Ry$ to $y$. \item ?p. 64? (Dwight Spencer) The diagram at the bottom should be labeled (1). (I don't think it is actually referred to, but the diagram numbering in this section begins with (2).) \item?p. 89} (Jim Otto) Refs Osius ?74, 75? are not in the bibliography (p 337). \item?p. 137? (Jim Otto) Theorem 5 has too few hypotheses and Proposition 4 too many to apply the latter in the proof of the former. There are various possibilities of getting it right, including adding the finite limits and colimits to the hypotheses of Theorem 5. But that theorem is true as it stands. Probably the best is to first point out first that only equalizers and coequalizers are needed and then only the $U$-contractible ones. Finally, if we suppose only the $U$-contractible coequalizers exist (any that exist will be preserved by a functor that has a right adjoint), that is enough to do Theorem 5 (Exercise, using the fact that the underlying functor of a tripleable functor creates limits) and from that will follow that the $U$-contractible equalizers exist. If we suppose that $\Bsc$ has $U$-contractible equalizers, the dual of Theorem 5 would imply that $U$-contractible equalizers exist. Hence sufficient for Proposition 5 is that {\em either\/} $U$-contractible equalizers or $U$-contractible coequalizers exist. Does anyone want to find an example to show that any completeness hypothesis is necessary? \item?p. 172? Second sentence: $\P$ having a left adjoint does not imply $T$ does. The sentence and following one should be combined as follows: ``Since $\T$ is the composite of a functor and its right adjoint, it is the functor part of a triple $(T,\eta:1\to T,\mu:T^2\to T)$.'' \item?p. 234? second paragraph (J\"urgen Kozlowski): Change Corollary 5 of Section 5.4 to Corollary 8 of Section 5.3. Also, Exercise CANON doesn't exist; delete the reference. \vskip1ex\noindent (Two missing references noted by J\"urgen Kozlowski): \vskip1ex\noindent G. Osius, Categorial set theory: a characterization of the category of sets. J. Pure Applied Algebra, {\bf 4} (1974), 79--119. \vskip1ex\noindent G. Osius, Logical and set theoretical tools in elementary topoi. Model Theory and Topoi, \lnm{445} (1975), 297--346.