How do you move the beginning of the table of contents, list of figures, and list of tables further up the page? The default is to start those sections above a third of the way down the page.

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Using the tocloft package (of course, instead of -2cm you can use the length that best suits your needs):

\documentclass{report}
\usepackage{tocloft}

\renewcommand\cftbeforetoctitleskip{-2cm}
\renewcommand\cftbeforeloftitleskip{-2cm}
\renewcommand\cftbeforelottitleskip{-2cm}

\begin{document}

\tableofcontents
\clearpage
\listoffigures
\clearpage
\listoftables

\end{document}

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What about the distance between the word "Contents" and the first entry of the TOC? – richtera Mar 6 '12 at 22:13
@AlexRichter: then redefine \cftaftertoctitleskip. – Gonzalo Medina Mar 6 '12 at 22:16
Thanks for all your help today! – richtera Mar 7 '12 at 0:29
What about the distance before (and after for that matter) the title of the "List of symbols" (LoS), "List of constants" (LoC) and "List of acronyms" (LoA) of the Glossaries package? For some reason these do not align with the LoF and LoT titles in my document. This looks bad in my two-page document since two of these titles are on opposing pages. My "List of symbols" title on the right page is about one row below the "List of tables" title on the left page. The LoF and LoT titles seem aligned with the ToC title, whereas the LoS/LoC/LoA titles seem to be aligned with the "Chapter" titles. – MLC May 6 at 17:30