Baking bread without yeast

If you want it to be bread, you will need some type of leavening. You can create a starter (think sourdough), which is essentially growing your own yeast and bacteria. This, of course, takes several days until it is useful. Alternately you can use a chemical leavener, like baking powder or baking soda. These obviously result in different types of bread.

You could look into making flatbread, which often (though not always) gets its name through being unleavened, and thus, flat (yes, I am oversimplifying here). Common examples are tortillas or roti.

Sourdough bread

Assuming by "not using yeast" you mean not using commercially bought yeast, you can make Sourdough bread; which relies on naturally occurring "wild" lactobacilli and yeasts

It is unclear what you are asking. If you mean...

Can I make bread without buying yeast from the store and adding it, and without the bread tasting yeasty?

...then the answer is definitely "yes". Sourdough bread works perfectly fine without added yeast - the reason being that the sourdough itself contains yeast microorganisms as part of its natural composition. In some countries, this is the primary way to make bread, and the strong yeasty taste of e.g. more Italian/French breads (baguette etc.) puts them in a quite separate category.

If, instead, you mean...

I am allergic to yeast, how to I make bread?

...then it gets a little complicated. There are some bread-like recipes which contain no yeast (and no agent to make it "fluffy") in any form, for example Roti or other flatbreads. Very tasty and easily made in a pan, but some people would not necessarily identify it as "bread" per se. Still, try them out and see if you like them. You can also play around with soda or other replacements, but it will be quite different.

You could also make

Smooth Bread

Which is apparently:

NO yeast NO flour

Three options, depending on exactly what you mean by "no yeast":

• No purchased yeast. In this case, you would make a sourdough starter, essentially cultivating your own source of wild yeast from your environment. You'd have a startup time of several days to a week before you could bake a loaf of bread this way. There are any number of directions for how to do this available online, especially these days; a reliable and easy-to-follow one is the King Arthur Flour recipe. Once you've established your starter you can bake a "regular" loaf of bread.

• No yeast at all, but a risen loaf. In this case you need to look into an alternative leavening like baking soda or beer. Looking for recipes for "soda bread" or "beer bread" will help you find something here. Beer is, of course, made using yeast, so depending on your reasons for avoiding yeast this may or may not be an option - there almost certainly won't be enough live yeast in your beer to act as a leavening agent (the leavening in beer bread comes from the carbonation), but if you have other reasons for avoiding yeast it may not be an option.

• Completely unleavened bread. This will limit you to flatbreads; not all flatbreads are unleavened, but some like chapatis and tortillas are.

Soda bread, which is bread made with baking soda as the leavener, is not that far from yeast-risen breads, and can be used in a similar fashion. The crumb isn't nearly as fine as that for a yeast bread, and so it's a bit closer to muffin texture in many ways (for obvious reasons), but it's not a terrible substitute - and it cooks far quicker than yeast breads (1 hour or so from start prep to finish, or even less if you make rolls or other smaller breads that cook faster).

The type of soda bread I prefer is Irish soda bread, or this one similarly - both are very simple, few ingredients (4-5 depending on if you have buttermilk or not).