
das Kapitel
chapter
A section in a book or another longer text, usually numbered or provided with a heading.
Lies bitte für morgen das dritte Kapitel.
Please read the third chapter for tomorrow.
chapter
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chapter
A section in a book or another longer text, usually numbered or provided with a heading.
Lies bitte für morgen das dritte Kapitel.
Please read the third chapter for tomorrow.

chapter
A section or phase in a person's life, in history, or in a development.
Mit dem Umzug in eine neue Stadt beginnt für sie ein neues Kapitel.
With the move to a new city, a new chapter begins for her.

to be a chapter of its own
A fixed expression meaning that a topic is especially complicated, extensive, or difficult and requires separate consideration.
Die deutsche Grammatik ist ein Kapitel für sich.
German grammar is a chapter of its own.
The meaning 'stage of life' is a metaphor. Life is seen like a book in which you begin new chapters or close old ones. This idea helps you understand the figurative meaning.
Nach der Trennung war es Zeit, ein neues Kapitel aufzuschlagen.
After the breakup, it was time to open a new chapter.
The idiom 'ein Kapitel für sich sein' (to be a chapter of its own) describes a topic that is so complicated or special that it has to be treated separately. The subject is the complex topic itself.
Die Steuererklärung ist jedes Jahr wieder ein Kapitel für sich.
The tax return is a chapter of its own every year.
In the metaphorical meaning, 'Kapitel' (chapter) is often combined with verbs such as 'beginnen' (to begin), 'aufschlagen' (to open, meaning to start something new), or 'abschließen' (to close, meaning to end something).
Mit seiner Pensionierung schloss er ein langes berufliches Kapitel ab.
With his retirement, he closed a long professional chapter.
When talking about a book, 'Kapitel' (chapter) is almost always used with an ordinal number (first, second, third...) to indicate the position in the text.
Die Lösung für das Rätsel finden Sie im letzten Kapitel.
You will find the solution to the puzzle in the last chapter.
phase
Phase mainly refers to a period within a development that is defined by both time and content. Kapitel frames the same period more strongly as part of a story that can be told, for example in a person's life. Use “Phase” for the progression and “Kapitel” when the story or a new section is the focus.

Nach der Krise begann ein neues Kapitel in ihrem Leben.
After the crisis, a new chapter began in her life.
Nach der Krise begann eine neue Phase in ihrem Leben.
After the crisis, a new phase began in her life.