Basic tools for digital filter design?
There are lots and lots of software that can aid you in designing digital filters. MATLAB is probably the most used software, at least in the university sector. The  DSP toolbox and the signal processing toolbox probably cover all of the well-known methods for digital filter design, as already mentioned.

Alternatives to MATLAB (that are free) include: Julia, Octave, Scilab, and SciPy (Python with libraries for technical computing). There are a lot of others, but these are the ones that I know have high quality libraries/methods for filter design.

For Julia, you can use the Filters.jl package, for Octave the signal package, for Scilab the Signal Processing toolbox, and for SciPy you have scipy.signal. 

A lot of filter design is done using optimization, and if you want to customize the cost-function or make other tweaks to e.g. the least-squares method or the Parks-McClellan method, you could have a look at a high-level optimization library such as CVX (works with MATLAB and Julia ++), or JuMP for Julia.

These are just the tools that I have a fair bit of familiarity with...