How to avoid lumps

How can you avoid those famous lumps?

Here's a list of possible actions:

1) If you're incorporating a powdery ingredient (flour, almond powder, etc.), you need to sift the powder in question before incorporating it.

In this way, you'll eliminate the "pellets" that inevitably form over time in a powder due to humidity. For some flours, such as chestnut flour, this is essential.
Don't hesitate to sift together several or all the powders in a recipe, for example for a cake: flour + sugar + yeast.

2) For mixing, use a whisk instead of a maryse, spoon or spatula, as it mixes much better.

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3) If, despite this, you're still faced with lumps, as a last resort, the mixer is your friend: giving your dough in preparation a good blow will liquefy it in a matter of seconds.

But don't use it on dough containing whipped cream or egg whites, as you'll destroy the airiness of the mixture.

What if it's not a powder you're mixing in?

You could have the same kind of trouble with a preparation where you incorporate butter or chocolate, for example, but it's a question of fat: you get lumps, of a different kind, but just as irritating.
You can use the same lifesaving gestures, but your problem probably stems from too great a temperature difference between the dough you're mixing in and the butter, and the latter congeals and clumps together.
The trick is to keep mixing, placing your dough in a bain-marie that's not too hot, or if possible, putting it in the microwave for 20-30 seconds.

To sum up: to avoid lumps with powders: sift, whisk, mix, and with fats: the same, but pay attention to temperature differences.