Off the top of my head (and relating the answer to the films, rather than the comics) there were a number of fields in which Tony Stark demonstrated outstanding knowledge
Engineering + Physics
Tony's arc reactor, the literal heart of the machine is a wonder of engineering, outputting a vast amount of electricity with no obvious source of fuel, potentially a form of fusion(?) and definitely containing plasma and magnetics.
Alongside this, he creates a workable augmented suit of armour, something that the finest minds at DARPA have struggled with for a generation
Flight Dynamics and Rocketry
Let's not brush aside the fact that Tony's suit can fly on tiny little jets that have no evident source of fuel. The output from those much be absolutely fabulous to lift a suit weighing the best part of a metric ton
Oh, and the suit appears to have some sort of g-damping technology that allows him to slam into walls and not die.
The suit has built in weaponry including rockets, modified guns, heat-seeking trackers, etc etc. At the very minimum, Tony would have to have an expert knowledge in how to make, maintain and install these weapons in order to have not killed himself many times over
AI + Computing
Tony's suit contains a realtime AI. An AI. Let's think about that for a second. A fully functional, turing-compliant Artificial Intelligence lives in the memory of his suit and can, apparently communicate with him in total realtime, organising his diary, arranging comms with third parties, planning routes, determining strategy and keeping an eye on radar.
Of all of his inventions, this one is the most epic.
Metallurgy and Armour Design
The armour on the suit is, as you've pointed out, completely bulletproof and regularly takes hits from uber-powered weapons and energy beams. The fact that it doesn't even come off dented would suggest a knowledge of ultra-light, ultra-strong alloys.
Bionics, Life Sciences and Medical
Tony's suit appears to be able to read his mind, assess his health (in realtime) and provide medical assistance when required. At the very least, he must have a full working knowledge of Neuroscience, anatomy, physiology and trauma medicine in order to have accomplished the feats we see in the films.