psoriasis

Hello. About two months ago I started to suffer from first symptoms. I felt really strong itchiness on my elbows and my knees. So, it looked kind a strange to me but I didn’t pay too much attention on it at that moment.
After a month or so, some more serious symptoms occurred. Some circular and oval shaped red plaques showed up which caused itchiness and burning sensations.
Please tell me what this could be? I'm 50 year old and I have never had problems of this kind.

From all the data you have mentioned I am thinking on only one disease that matches all your symptoms- Psoriasis.
Psoriasis is a common and chronic skin disorder and the plaques or patches you have mentioned are the usual sign.
The patches are usually found on the arms, legs, trunk, or scalp but they can be found on almost any part of the skin.
You didn’t mention are there any cases of psoriasis in your family and this could very important because psoriasis is not contagious but can be inherited. So, you should contact your dermatologist as soon as you can so he could take a skin biopsy and set the right diagnosis.