Short version of a long story: I happen to know this software quite well although I have personally never used it.
Mathematica is a product of
Wolfram Research, an Illinois / USA based company. They do not have free products available. To use the additional packages you first need to install (buy) the underlying Mathematica software.
Mathematica is available as a quite limited home version for non-professional hobbyists at €295 / £195 / $295 + VAT (one year licence €149 / £95 / $149 + VAT). The standard
Starter version costs €1,270 / £815 / $995 + VAT.
A limited
Student Edition is also available, costing €154 or €54 for one year licence or €35 for one semester licence. The Student Edition prices mentioned here are for Euro region and including the VAT. I do not know the prices for Student Edition in other regions.
If you have a possibility to use an USA based delivery address, it's worth to use it as the Wolfram's pricing policy is very strange; the US prices are clearly lower than European / UK prices. The difference and possible savings are especially big when buying the Starter version, for example as per todays official exchange rates the US price is over 40% cheaper than the Euro price.
Wolfram Mathematica Webstore:
https://www.wolfram.com/mathematica/how-to-buy/industry-individuals.html
Kari