RaspberryPi as a NVR solution

Recently, one of my close relative wanted to install a security plan into his house using a CCTV solution (closed circuit television aka video surveillance). We got some quotations which were clearly out of budget for us (the lowest price was 1300€, including 4 cameras, a NVR box and the setup).

My challenge was to cut the price at least by 2, including the hardware, the software and the setup. The underlying benefit is also to explore and to learn.