"Undefined variable", "Undefined index", "Undefined offset" errors in PHP: how to fix

Hello everyone! I'm a beginner in PHP and constantly encounter errors like Notice: Undefined variable, Notice: Undefined index, and Warning: Undefined array key. They are displayed on the screen and break the logic of my code. Help me understand what they mean and how to get rid of them.

Here is an example of code that causes an error: I'm trying to get data from a form:

<?php\n    $name = $_POST['username'];\n    echo "Hello, " . $name;\n?>

If the form is not submitted, then Notice: Undefined index: username appears. And if I simply use a variable without checking:

<?php\n    echo $message;\n?>

Then I get Notice: Undefined variable: message. Also, sometimes when