Remove "Abstract" title from Abstract

\renewcommand{\abstractname}{\vspace{-\baselineskip}}

Slightly more economical than the proposed solution (no need for abstract package).

The simplest way is

\usepackage{abstract}
\renewcommand{\abstractname}{}    % clear the title
\renewcommand{\absnamepos}{empty} % originally center

The title is stored in \abstractname, so we clear it; but abstract puts the title between \begin{center} and \end{center}, but actually center is stored in the macro \absnamepos; so we abuse LaTeX features and place the (empty) title in the (inexistent) empty environment so the result is that nothing will be printed and no excess space will be set.