I went to UK and back previous week. I have a multi entry visa. Can I use this visa to enter UK for a second or third time? Do I have to inform some authority about it beforehand?
Yes, if you hold a multiple entry visa you can use it for multiple entries within its validity period.
You don't need to make any special notification in advance. Like when entering for the first time, you should expect to be asked about your plans at immigration on arrival. It would be wise to carry documentation of travel/accomodation arrangements, and anything else that might be relevant to demonstrate that your plans for the visit comply with the visa rules.
A multi entry visa was created exactly for this purpose - to enter a country wihtout applying for another visa. You should not inform any authority about your next trip, but you should be prepared for some questions on arrival (which may be asked or not).