A popular company that does this is Intrepid Travel .
They do group tours everywhere including Europe.
Just make sure you change your country of residence down the bottom of the page if it is not correct already.
travel.stackexchange.com/users/1053/Craig Curtis
Since you are Italian, you may want to give Avventure nel mondo a try.
It is a well known site that perfectly fits your needs.
If I can give you a piece of advice, don't understimate travelling alone.
It's one of the best ways to meet other people during your trip, not only other travellers but local people too.
Being alone makes you more responsive to people around you and you will be more inclined to talk with them.
Even if in your country you are not the kind of person that can easily approach other people, it will surprise you to find out how easy it is to do that while travelling alone.
travel.stackexchange.com/users/2523/Geeo
Contiki is another company that does group trips, though for a limited age range (18-35).
They have tours on several continents, including Europe.
I haven't personally used them, but know of people who have and
they were very happy with the trip.
They called it exhausting, but the time of their life.
travel.stackexchange.com/users/2823/Mari
Couchsurfing can be used to do something like this: the site includes city-specific forums.
Using these forums you can meet up with other travelers who are visiting a particular city.
travel.stackexchange.com/users/349/nibot
Honestly, I am surprised at the question.
This is how the majority of tours work.
There are thousands of companies offer tour all around the world.
All you have to do is Google Search a desired destination plus the word tour .
It can be as specific or a general area are you like:
Europe tours Spain tours Madrid tours Tours where you are not travelling with other people are generally called private tours which are much more expensive because costs are not shared between so many people.
Also, when looking at tours, group tours have specific dates stated since people must travel together.
Highly popular tours can run each week and less popular (or very expensive) ones can have only one or two dates per year.
Most group tours do not include airfare to where the tour starts and from where it ends.
So try to arrive one or two days before not to miss a tour which goes out far the very first day.
For example, tours to Machu Picchu usually pick up participants in Lima and fly the next day to Cusco, so if your flight gets delayed, then it is difficult to catch up.
Since you stated your goal is to meet people, you can do improve your odds of encountering people you can relate to by looking for a specialty tour of your interests.
Example of those are photography tours , culinary tours , adventure tours , cycling tours , etc.
They even have singles tours where people who participate are usually single.
Some companies even have tours where the goal is to meet locals.
Usually they include stays with local families, rather than hotels.
This can be fascinating and they can teach you local cooking, crafts among other things.
If that interests you search for local living or home stay tours.
travel.stackexchange.com/users/4801/Itai
A bit late to help the OP, but maybe useful for others who read this question and its answers.
HF holidays is very good for walking and other activity holidays in the UK (also for foreigners) and in Europe (which will suit the British more than people from outside the UK.)
As a solo traveler who loved walking but not alone, I did enjoy staying with them some time.
I am just a happy customer, not involved with the organization at all.
travel.stackexchange.com/users/27650/Willeke
Are there any online resources that help in organizing group travels?  Perhaps a site with a bunch of trips that people can join and if they join they are going to travel with the company of new people who have booked the same trip. In other words a vacation which allows you to meet new people.   I'm from Italy and I'd like a European trip.
How can I participate in group travel?
travel.stackexchange.com
<online-resources><group-travel>
travel.stackexchange.com/questions/8550
travel.stackexchange.com/users/2819/Luigi Tiburzi
Many companies offer group tours around the world, and you could try Intrepid Travel, Avventure nel mondo, Contiki (for travellers aged 18-35) or HF Holidays (for walking and other activity holidays in the UK and Europe). Couchsurfing also includes city-specific forums that could be used to organise this, or you could Google a desired destination plus the word  tour. Many companies offer tours in different countries. These can easily be found on Google searching the destination name plus the word tour.
There are many companies offering tours in many different countries. Serach for tours on Google using the name of the destination plus the word tour.