You first of all have to announce babel you want to use Italian in your document, so do
\usepackage[italian,british]{babel}
that still makes British English the default language for the document.
You now have available several possibilities:
\selectlanguage{italian}, which sets Italian as the default language from the point of declaration on, respecting grouping.
\begin{otherlanguage}{italian}...\end{otherlanguage}, that's the same as before, but limits the scope of the language change.
\begin{otherlanguage*}{italian}...\end{otherlanguage*}, much similar to the above, but doesn't change the meaning of tags such as \abstractname or \chaptername.
\foreignlanguage{italian}{frase in italiano} for short inserts.
The main application you have in mind, perhaps, is for the abstract. So you can do (under \frontmatter, in order to have unnumbered chapters that go in the table of contents nonetheless)
\chapter{\abstractname}
The abstract in English.
\begin{otherlanguage}{italian}
\chapter{\abstractname}
Il sunto in italiano.
\end{otherlanguage}
Inside the document otherlanguage* is probably the environment you'll choose.
Some notes about your preamble.
The package ae is obsolete; don't load it.
Also subfigure is deprecated. Its official substitute is subfig, but it's more recommended to load subcaption. Both require syntax changes (check the manuals), but are better and, especially subcaption, more powerful.
Whenever I see a table using \multirow, I always find a better way to make it without the command. But this is personal opinion. `;-)
Here's a polished up version:
\documentclass[12pt,a4paper,titlepage]{book}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[british]{babel}
\usepackage{subcaption}
\usepackage{amsmath}
\usepackage{amssymb}
%\usepackage{multirow} % please! ;-)
\usepackage{verbatim}
\usepackage{alltt}
\usepackage[italian,british]{babel}and then\begin{otherlanguage*}{italian}testo in italiano\end{otherlanguage*}. Unrelated: remove the call of theaepackage: it has been obsolete for several years and has several limitations. Alsosubfigurehas been deprecated: loadsubfigor, better,subcaption. Both require syntax changes, but they are definitely better (the second one is recommended). – egreg Oct 07 '15 at 19:57