SLEPc is a software package that provides functionality for solving a variety of eigenspectrum problems, both standard and generalised. It relies on various different sparse and dense matrix and vector formats that are defined in the PETSc package. Naturally, this means PETSc must be correctly installed before a working copy of SLEPc can be installed as described here.
deal.II has wrapper classes to the solver and spectral transformation parts of SLEPc that loosely provide almost the same interfaces as the wrapper classes to the PETSc functionality. They are used in a simple case in step-36.
      SLEPc requires the environment variables PETSC_DIR
      and PETSC_ARCH to be set already and usually
      requires you to set the environment
      variable SLEPC_DIR as well. If the environment
      variable is set, then
      deal.II will pick up on this during
      configuration; just as before with PETSc.
    
      Alternatively, the -DSLEPC_DIR=DIR option
      for cmake can be used to override the values
      of SLEPc_DIR if, for example, these environment
      variables are not set at all. You can also
      specify -DDEAL_II_WITH_SLEPC=OFF as a flag during
      configuration to have deal.II completely
      ignore a SLEPc installation.
    
Note: The version numbers (x,y,z) of your SLEPc installation must be identical to the same version numbers of your PETSc installation.
      Installing SLEPc is not much of a challenge once PETSc has been
      correctly installed (check this first!). What is happening here,
      is that SLEPc scans your PETSc installation and figures out how
      that was configured; its location, the
      given PETSC_ARCH, MPI settings, debug
      mode, and so on.
    
This builds a simple SLEPc installation:
	tar xvzf slepc-x-y-z.tar.gz
        cd slepc-x-y-z
	export SLEPC_DIR=`pwd`
	export LD_LIBRARY_PATH=$SLEPC_DIR/$PETSC_ARCH/lib:$LD_LIBRARY_PATH
	./configure
	make
      
      Now let SLEPc check his own sanity:
      
	make test
      
      will self-check the serial (and MPI) implementation of SLEPc.
    
    
      Finally, you may want to put the two export
      commands above into your ~/.bashrc
      or ~/.cshrc files, with the first one replaced by
      
	export SLEPC_DIR=/path/to/slepc-x-y-z
      
      The cmake installation should then be able to pick
      up where you installed SLEPc and include it automatically in the
      deal.II build without any further need for instructions. You
      will see at the bottom of the cmake output if that
      is what actually happened.