If you want to directly come to Tabriz from Europe, a convenient option is to change flights in Istanbul. There are regular flights from Istanbul to Tabriz airport. Information about flights to and from Tabriz airport can be found here. As you see, there are flights from Tabriz to other touristic beautiful cities of Iran like Isfahan, Shiraz, Kish,  Mashhad and Ahvaz as well as industrial and commercial sites in Iran like Asalooye and Mahshahr. There are direct flights to Tabriz from Dubai and Baku and a couple of other cities.

Of course there are also several flights to Tehran everyday from Tabriz but I want to suggest you another route to travel between Tabriz and Tehran which in my opinion for a tourist who wants to explore Iran is more interesting. There is a high-way between Tehran and Tabriz. Distance is about 700 km. It is not common in Iran to rent a car but there are very modern and comfortable buses travelling between Tehran and other major cities like Tabriz, Isfahan and Shiraz. You should ask for so-called VIP buses.

If you come from Tehran to Tabriz I suggest you to stop for a few days in Zanjan, too. Zanjan is a very beautiful city. It has interesting places to visit, including Soltanieh dome and Katale-khor cave.  From Zanjan to Tabriz if you take the high-way you will see the colorful hills such as the one below.

If instead of the highway you take the old road, you pass city of Miyane and you will encounter the following bridge which is known as "Ghiz Korpusi" in Azarbaijani Turkish which is also known as "Pole-dokhtar" in Farsi. Both mean "Girl's bridge." I do not know when and by whom the bridge is built in the first place but I know that a Tabrizi Princess in 14th century has had it repaired and maintained. In 14th and 15th century, Tabriz was the capital of Kara Koyunlu dynasty. Several monuments remain from that dynasty that have been commissioned by  queens and pricesses of that dynasty. There are even smaller ones donated by rich female merchans of that era.   Because of its strategic importance, the middle part of the bridge was exploded by a mine in 20th century after WWII.

Closer to Tabriz you will visit this beautiful lake called "Ghuri Ghol."

From biological point of view, this lake is important. It houses 92 species of birds and several species of mammals and reptiles. Some of the birds emigrate to this lake from as far as Siberia. Some of these species are in the danger of extinction and are therefore protected. Last year a new bacteria was found in the lake. The bacteria was called "Alishewanella Tabrizica." Half jokingly, in honor of "Alishewanella Tabrizica", I celeberated by throwing a reception in my workplace which is a research institute of physics (not biology!)