Dear Debian users/developers,

I'm using Debian 8.1 on one of my computers. It's easy to use and (as far as I can see) rock solid!
On my other computer I use ubuntu 14.04 and dual boot with M$ windows 10. Ubuntu 14.04 is full of bugs and the most unstable OS I've met (with the exception of M$ windows, of course). Now I want to replace Ubuntu with Debian. Now, my question is: Do I risk the windows installation when "writing over" Ubuntu with Debian?
(I sometimes need the windows installation in my job to run applications my employer forces me to use).

As long as you don't touch the Windows drive, or the EFI drive (if you have a UEFI firmware), then no, there is no danger of damaging Windows when overwriting Ubuntu.

Have you installed many Linux distributions, particularly dual or multi-boot? It should not be that difficult and as pointed out above, the method will vary depending upon whether you are using UEFI (especially since you are using windows 10) or MBR to boot. Install Debian to the same partition on which you have Ubuntu, make sure you select to format that partition during the install. I don't use Debian but I'm sure there site will have installation instructions in detail.

https://www.debian.org/releases/stable/installmanual

You can use the debian partitioner to erase the ubuntu partitions, then select "Guided Partitioning, Use Most Contiguous Free Space" to install debian.