Calendar

On my phone I use Business Calendar 2, for birthdays, my work schedule and other events to keep in mind, I would like to add something very similar in my sidebar, is there a way I can do this?

The app I use on my phone colorcodes the categories (for instance, my work schedule I have set to orange), and it’s set monthly in a grid where if you’d click/hover on a particular date and it gives that date’s (if something’s set) info.

Is there a plugin/script I could use to do something like this on my site?