Why so many transaction send bitcoins to the sender? While browsing the blockchain I noticed that there are a lot of transactions that send bitcoins to the sender (most part of the transaction) and a tiny fraction to another address.

E.g. this transaction sends more than 99% to the sender and the rest to another address.

What is the purpose of those kind of transactions?
An output of a previous transaction can only be spent wholly. So if you have 3BTC and want to send 0.5 to someone, you make a transaction that sends the 0.5 and then 2.5 back to your own address. This is called "change", just like you get change when paying in the supermarket, except in this case you give the change to yourself so you don't need to worry about the other person running of with it.

Note that this change address is supposed to be a brand new address (owned by yourself) and NOT the same address. Address re-use is bad for privacy: as you've just discovered you can in those transactions easily determine which part of the transaction was change and which was actually sent to some other person.