A few key points to make sure that the situation and context are well understood:
- Aggression is not a problem that gets fixed. It is managed and you measure improvement over (long periods of) time
- Agression toward other dogs is called intra-specific aggression (dog-dog aggression, different from dog-human aggression)
- Such aggression can have basically two origins: (learned) fear aggression (your dog had bad experiences in the past and figured out that aggression was an appropriate response, plus it makes him feel better), (learned) resource guarding aggression (competition over food, available female dogs, etc.)
- Don't react aggressively to aggressive behaviors. That will only make things worse
- Aggressive dogs require more than just "training". You need advice from a veterinary behaviorist, not just from a regular dog trainer. My advice in this answer is not meant to be a replacement to professional help
- You said "he pretends he's not listening": he's truly not listening, his brain is off, he's so excited he can't learn anything and it takes time (minutes, hours) to recover from such an event. Remember last time you had a car accident and you were shaking, nothing people could say would make that disappear, it takes time to recover.
Prevention is very important
Aggressive dogs are at very high risk of being sent back to a shelter or being euthanised. It is your role to take actions to prevent that from happening.
As suggested in the comments, keep him on leash all the time, with a muzzle and do your best to prevent aggressive behaviors or aggressive displays to happen.
Training has to be done when your dog is not (yet) aggressive! When he goes "out of control" it is way too late to address the problem. His brain will be "flooded" by neuro-chemicals, and that suppresses almost any learning capability. Anything you'll do at that moment will have very little effect, your communication with your dog will be close to zero, everything will be wrongly/poorly understood and the chances are that it will make things worse.
Meeting aggression with aggression leads to even more aggressive behaviors. Additionally there's the risk of transforming dog-dog aggression into dog-human aggression which is even more difficult to manage.
So again, take all the necessary steps in advance, have a clear plan of what to do when you meet another dog. Don't get sentimental about restricting his "freedom": you'll live with him for the next 10 years, keeping him on a leash with a muzzle for 1 year and taking proactive actions will help him a lot, reduce the risk and will most probably allow you to deal with a much easier situation in the next 9 years.
What solutions do we have?
Many elements of this answer come from Karen Overall's book Manual of clinical behavioral medicine for dogs and cats from which I extracted bits and pieces.
Steps towards counter-conditioning
The very basic idea is to train alternative behaviors which will allow the dog to progressively control its reaction while next to other dogs. First these alternative behaviors are trained to make the dog react in a more appropriate way and to set him up for success while rewarding appropriate attitudes.
These are my words. I like to talk about behaviorial training and attitude training. An example makes it very clear: first you train him to sit when he sees another dog. That doesn't suppress his urge to "attack", but at least you have a behavior which is incompatible with him moving towards the other, additionally sitting will make it easier for him to relax and with training evolve to non-aggressive attitudes.
That training has to be done in a way that you start well below its aggression threshold: you first start 100 meters away from another dog, he sees it, doesn't react, you click and treat (*).
Stay at that level and progressively train him to sit or lie down automatically as he sees another dog. When you get that, rewarding all the time, make it (very) progressively more difficult by getting closer to other dogs.
Make sure to do it slowly. You want him to stay relaxed, see my comment above about "brain chemistry".
Sitting or lying down will help him increase its reaction threshold. Keep rewarding him while he sits/lies down. Progressively you'll notice that he "recovers" faster and faster after seeing another dog, reward that. Now you are not just training him to sit, but you're reinforcing its calm behaviors.
Get closer and closer to other dogs. Always make sure that he's successful. It can take weeks or months.
Remember that training is not about testing the dog: don't practice the above exercise 3 times and then go to central bark to see if he improves! A successful training session is 2 steps in the right direction, a situation where he gets aggressive is 1 step in the wrong direction, if not more than 1.
This gives you a rough idea of what a behavioral modification program can look like. A veterinary behaviorist will guide you more precisely.
What about drugs?
I don't want to cite anything specific as this goes well beyond my actual knowledge. Seek professional help.
There are different classes of drugs in veterinary medicine that can greatly help with anxiety disorder. As said above, aggression can be fear-related.
It is very useful to introduce drugs into a behavioral modification program from the beginning. Again, we want the dog to learn, and that requires a correct neuro-chemical state.
Drugs are a complement and allow you to be more successful. They are not supposed to cure the problem or make it disappear.
Get involved in some training with your dog
Rescuing a dog and addressing an aggressive behavior is like learning a new language and being interviewed on TV. Super difficult and not a great experience.
My point is: learn about dog training (see below) and train him at home, start with "trick" behaviors. That will help you better understand training, it will connect you with your dog. It will have fun and even more willing to solve the other problems.
I think this will have two key effects in your situation:
As you need to prevent aggressive behavior from happening, you might need to change your walks schedule and/or reduce them. To dogs mental stimulation is as important as physical exercise. Additionally your dog was used to think a lot: looking for food, not being killed by a car, etc. Positive reinforcement training makes him thing. A 15 minute training session is worth a short walk. I'm not suggesting that it replaces physical exercise, but it is a very good complement.
Your dog is reacting to its environment and in a new situation takes cues from the environment (sniffing around, exploring, etc.) Training and/or play will teach the dog that he also has the possibility to take cues from you. That's very important.
References
I suggest you have a look at this book.
(*) That's in the framework of clicker-training. I suggest that you have a quick look at what it means. That's a powerful and fun way to train dogs. If you don't just consider that "click and treat" means "give him something he likes", food is great, a toy is good also but most of the time giving food is easier.
