Where should I start to learn game development?

Well I'm not discouraging you, But One learns how to write games by writing games, I mean code and learn, code and learn and learning by doing it yourself is the best way.

Before Getting into games I would suggest you to have a Good Study on computer graphics, mathematics related to graphics, Data structures and Algorithms.

• Start with a programming language that is easy to use (easy to use for you most importantly and some times it is need to be chose as per target platform) I'll suggest start learning Unity 3d Game Engine for fast prototyping games.
• Get a beginners book for that programming language
• Decide on some API or environment that provides what's needed for writing games. I started out by doing snake, space invaders etc in the console, but any 2D-environment will do (stay way from 3D for as long as you can; there are much more important things to learn first). SDL/GLUTfor OpenGL has bindings in almost any language. Pygame for Python looks promising too. UsingHTML5's canvas-element, you could even write the programs in the browser using JavaScript. Im not sure what's best these days, but there you have some suggestions.
• Find a community for inspiration and help when stuck. I used gamedev.net. Since we're on stackoverflow, gamedev.stackexchange.com should also be a natural choice :)
• Start small. Very small. I mean really tiny. Then take small steps to new challenges. Please don't go for big game say MMORPG.
• The game design and graphics are fun, but focus on the programming (for now at least). When you've written a simple game, learn how to do the same thing better.
• Set a goal. Imagine the game that you'd want to make. Don't try to make that one immediately, but make sure that each new thing you learn or make takes you one step closer. Don't learn what you don't need.
• Follow some tutorials. Honestly, even if you have no intention of being a coder, follow a Unity tutorial to understand how things work.
• Ask yourself what you want to do. If you want to be an all in one development indie powerhouse, you have a lot to learn. If you want to be a great artist (for example), acknowledge that and learn from the experts in your field. While a broad understanding of the whole process is a definte plus, focus your efforts into what you want to do where possible.
• Remember there are people whose career is to tell people like you what you need to do to get into game dev. You don't need to talk to them. Just research, learn, and create. Approach studios directly. Advice and a guiding hand is great, but find the passion and drive from within. I'm not saying don't use agencies - but don't solely rely on them.

You learn by doing. I've "learned" Unity game development  making my own games over last 5+ years.  It's not about process, or knowledge, or qualifications, but articulating your inner game designer into a set of repeatable rules that everyone can experience.