Hey Hermine,
Thanks for reaching out!
The features you describe, where users click on a category to filter by that category, are NOT provided by Events Calendar Pro. Filter Bar is the best plugin of ours for this; you can install it on your site alongside The Events Calendar—you do not need Events Calendar Pro to use it!—and then once installed, it will offer the sort of category filtering you describe.
To see these filters in action, I would recommend exploring our demo site a bit: http://wpshindig.com/events
While things on that events page like the Map View and Photo View are only possible within Events Calendar Pro, the basic filters that I highlighted in this screenshot with an arrow are what come “out of the box” with Filter Bar:

So, check out the demo page and play around with those filters, and let me know if there’s anything else I can help with!
Sincerely,
George