/!\ kodi is available in jessie-backports so this page isn't needed to install kodi on jessie.

/!\ Since kodi is available in Debian now, a better way to build from source is to build using apt.

This page describes how to build Kodi 15 (Isengard) for Debian jessie (amd64, may work for i386 too).

Install packages for building

sudo apt-get install git build-essential equivs

Download Isengard sources

git clone -b Isengard git://github.com/xbmc/xbmc.git

Install build dependecies

First create a text file control with the following content:

Section: misc
Priority: optional
Standards-Version: 3.9.2

Package: kodi-15-build-deps
Depends: autoconf, automake, autopoint, autotools-dev, cmake, curl, default-jre, gawk, gperf, libao-dev, libasound2-dev, libass-dev (>= 0.9.8), libavahi-client-dev, libavahi-common-dev, libbluetooth-dev, libbluray-dev (>= 0.7.0), libboost-dev, libboost-thread-dev, libbz2-dev, libcap-dev, libcdio-dev, libcec-dev, libcurl4-openssl-dev | libcurl4-gnutls-dev | libcurl-dev, libcwiid-dev, libdbus-1-dev, libfontconfig-dev, libfreetype6-dev, libfribidi-dev, libgif-dev (>= 4.1.6), libgl1-mesa-dev | libgl-dev, libglew-dev, libglu1-mesa-dev | libglu-dev, libiso9660-dev, libjasper-dev, libjpeg-dev, libltdl-dev, liblzo2-dev, libmicrohttpd-dev, libmodplug-dev, libmpcdec-dev, libmpeg2-4-dev, libmysqlclient-dev, libnfs-dev, libogg-dev, libpcre3-dev, libplist-dev, libpng12-dev | libpng-dev, libpulse-dev, librtmp-dev,libsdl2-dev, libsmbclient-dev, libsqlite3-dev, libssh-dev, libssl-dev, libswscale-dev, libtag1-dev (>= 1.8), libtiff-dev, libtinyxml-dev (>= 2.6.2), libtool, libudev-dev, libusb-dev, libva-dev, libvdpau-dev, libvorbis-dev, libxinerama-dev, libxml2-dev, libxmu-dev, libxrandr-dev, libxslt1-dev, libxt-dev, libyajl-dev (>=2.0), lsb-release, nasm, python-dev, python-imaging, python-support, swig, unzip, uuid-dev, yasm, zip, zlib1g-dev
Description: List of packages that are used to build Kodi.
 List of packages that are used to build Kodi.

Then create and install a package that will automatically install all Kodi build dependencies:

equivs-build control
sudo gdebi kodi-15-build-deps_1.0_all.deb

You can remove kodi-15-build-deps after you built Kodi and then run sudo apt-get autoremove to remove all installed build dependencies.

Configure sources

cd xbmc
./bootstrap
./configure --prefix=$HOME/local/

--prefix=$HOME/local/ instructs the installation program to install Kodi into local subdirectory of your home directory.

Compile

make -j4

-j4 starts 4 parallel compilation processes (the more processes, the faster is the compilation). For a dual core set it to 2.

Install Kodi

make install

Kodi will be installed in the directory specified during the configuration (See Configure sources)

Run Kodi

If Kodi was installed inot $HOME/local/ you can run it with the following command:

$HOME/local/bin/kodi

References

https://github.com/xbmc/xbmc/blob/master/docs/README.linux