Check the latest version here At the time of writing, 3.8.0 is the latest and 3.8.5 has release candidate.
Also make sure you have sqlite3, libbz2-dev and libffi-dev are installed
sudo apt-get install libsqlite3-dev libbz2-dev libffi-dev
version=3.8.5
wget https://www.python.org/ftp/python/${version}/Python-${version}.tgz
tar xzvf Python-${version}.tgz
cd Python-${version}
# Linux (or any Unix-like system), the default prefix and exec-prefix are /usr/local.
# thus you should be able to omit --prefix here
# --enable-optimizations option for significant speed boost (10-20%) but much
# slower build process
./configure --prefix /usr/local --enable-optimizations
make
sudo make install
# OR if you want to skip creating the python link then:
sudo make altinstall
in case you want to remove and re-install it again cause some software was missing before installation
rm -f /usr/local/bin/python${version}
rm -rf /usr/local/lib/python${version}
Cheers!