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First of all - Avogadro is packaged in all supported Ubuntu versions.

But if you really need to compile it, then:

  1. Enable source code repositories from Software & Updates (software-properties-gtk) and then reload repository information.
  2. Install development tools

    sudo apt-get install build-essential
  3. Get its build dependencies from the repositories:

    sudo apt-get build-dep avogadro
  4. Get and compile the source code of bionic (18.04 LTS) package

    git clone https://git.launchpad.net/ubuntu/+source/avogadro
    cd avogadro
    git checkout ubuntu/bionic
    mkdir build
    cd build
    cmake ..

but it will not compile with errors:

[100%] Linking CXX shared module ../../../lib/Avogadro.so
CMakeFiles/python-module.dir/swig.cpp.o: In function `Molecule_OBMol(Avogadro::Molecule&)':
/home/user/avogadro/libavogadro/src/python/swig.cpp:554: undefined reference to `OpenBabel::OBMol::OBMol(OpenBabel::OBMol const&)'
/home/user/avogadro/libavogadro/src/python/swig.cpp:554: undefined reference to `OpenBabel::OBMol::~OBMol()'
/home/user/avogadro/libavogadro/src/python/swig.cpp:554: undefined reference to `OpenBabel::OBMol::~OBMol()'
collect2: error: ld returned 1 exit status
libavogadro/src/python/CMakeFiles/python-module.dir/build.make:990: recipe for target 'lib/Avogadro.so' failed
make[2]: *** [lib/Avogadro.so] Error 1
CMakeFiles/Makefile2:3301: recipe for target 'libavogadro/src/python/CMakeFiles/python-module.dir/all' failed
make[1]: *** [libavogadro/src/python/CMakeFiles/python-module.dir/all] Error 2
Makefile:149: recipe for target 'all' failed
make: *** [all] Error 2

So it seems to be impossible.
Consider to try older version or upgrade the whole Ubuntu to 18.04 LTS.
Other options: create Docker container or schroot for this application with 18.04 LTS.