The minimum ingredients to make ("western") tasting bread are:
You would also need, albeit they are not considered ingredients:
- Air (*)
- A source of heat (usually an oven, but can also be a pot (such a Dutch oven), or some weirder for non so "western" breads).
When you give time to your mix of water and flour, you will get a culture of yeasts and bacteria. That culture has different names by different people: levain, starter, sourdough, biga...
It is important to note most of these yeasts and bacteria come with the flour, and they can perfectly rise your bread.
It wasn't until the identification of yeasts with microscopes in 1800s, when Saccharomyces cerevisiae yeast was taken apart from beer maker's cultures, and grown specifically. Beer makers also fed their cultures with just flour and water.
When you add a packet or a cube of yeast to make your bread dough, you are adding a culture of yeasts selected to enhance the grown of the dough.
I marked Air with an (*) because I'm not sure it is really essential. It can give some yeasts and bacterias to the culture, but flour has enough of them initially. And yeasts can grow and reproduce in 2 ways: aerobically and anaerobically. That is: with or without air. I've seen pictures of doughs grown in vacuum, but I'm not 100% sure if you could do all the process of starting your culture and rise the dough with absolutely no air at all.
To conclude: you only need water and flour (whether wheat or rye) to make a traditional loaf of bread. It might taste strange to most people today as it has no salt. But salt wasn't added to bread until 200 years ago (or so).
Specifically, you do not need for making bread:
Salt began to be used in bread less than 2 centuries ago. It began to be used not to give [salty] taste to the bread, but to make the dough easier to handle; due to its hygrostatic properties it makes the dough stiffer. Nowadays several traditional bread are made with no salt at all, like Mallorca (Spain) or Toscana (Italy) bread. And they are bread people eat every day.
See this answer on reducing amount of salt in bread, although I don't agree with him on taste. I think reducing salt brings up cereal flavours that were hidden. I guess it depends on the flour you use.
Saccharomyces cerevisiae yeasts eat sugar. In fact that's what "Saccharomycea" means: "sugar eater". Flour has enzymes that decompose starches in glucose, but it needs time to do so. If you add a lot of commercial yeast, it might not have enough sugar to work. So some recipes add sugar to allow yeast to have plenty of food. Malt are enzymes, so the time it takes to break down starch in glucose gets reduced.
See What is the purpose of sugar in making bread and Making malt free bread
You can have enough rising power with just levain/starter/sourdough.
See What is a culture in bread