In the past, we've looked at how lassen expresses "to let" and "to leave," and how lassen is used in combination with other verbs. But there are also many verbs that use lassen as a root. 

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This is by no means an exhaustive list, but instead a number of examples that are very common. Let's go alphabetically, starting with (jemanden) entlassen, which can refer to releasing someone from an obligation, but also is a polite way of talking about firing someone from a job. 

Eigentlich hätt ich ihn entlassen müssen.

Actually, I should have fired him.

Caption 53, Großstadtrevier: Nicht mit mir

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The verb (etwas) hinterlassen means "to leave (something) behind."

Aber wenigstens hat dieser Vollidiot eine Spur hinterlassen.

But at least the complete idiot left behind a trace.

Caption 59, Die Pfefferkörner: Endspurt

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The verb loslassen means "to let go," either physically or emotionally. 

Trotzdem weiß sie, dass sie ihre Kinder auch irgendwann loslassen muss.

But she knows that she must someday let go of her children.

Caption 43, Tapetenwechsel: Barbara Becker mag es aufgeräumt

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The verb nachlassen refers to something abating, fading, easing, or relenting.

Deswegen hat's in den letzten Wochen bisschen nachgelassen... in den letzten Jahren.

That's why it's declined a little over the past few weeks... over the past few years.

Caption 15, Formel-1-Rennfahrer: Timo Glock

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The verb (etwas) veranlassen means "to arrange (something)."

Ja, das können wir für Sie veranlassen.

Yes, we can arrange that for you.

Caption 74, Galileo: So hart ist der Job im Callcenter

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One essential verb is verlassen, which is different from lassen in that it specifically means "to leave" in the sense of departing from a place or abandoning someone or something. It also requires a direct object.

Ich möchte Sie bitten, dann die Fähre zu verlassen.

I would like to ask you to then leave the ferry.

Caption 19, Die Pfefferkörner: Abschied tut weh

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Ich will ihn auch gar nicht verlassen.

I really don't want to leave him.

Caption 69, Die Pfefferkörner: Abschied tut weh

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And finally, we come to zulassen, which means "to permit" or "to allow." 

Aber Theresa, wir können nicht zulassen, dass die beiden gewinnen.

But Theresa, we can't let the two of them win.

Captions 23-24, Heidi Schatzdiebe

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Einundsechzig Komma fünf Millionen Kfz sind in Deutschland zugelassen.

Sixty-one point five million motor vehicles are registered in Germany.

Caption 2, Richter Alexander Hold: Richtig parken

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Further Learning
You can find examples of these verbs, as well as others that have the root lassen, on Yabla German. One additional expression you can look up is sich auf jemanden verlassen. 

How do you say "I don't mind" in German? At the end of the recent lesson about the verb ausmachen, I mentioned that the verb ausmachen, combined with a dative pronoun and the negation nicht, is a way of asking if somebody "minds" something, or of stating that "you don't mind."

Ach, was soll's! Die Alten meckern ja dauernd, aber das macht mir nichts aus.

Oh, never mind! Old folks are always complaining, but I don't mind.

Captions 19-20, Es war einmal... der Weltraum Die Saurier

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The adverb meinetwegen is a curious one. It may be translated, according to the context, as "for all I care," "because of me," "as far as I'm concerned," or even just "whatever." But sometimes it's also "I don't mind":

Meinetwegen. Aber wenn du das Geld von meinem Vater hast, dann sag...

I don't mind. But if you got the money from my father, then say...

Captions 38-39, Die Pfefferkörner: Endspurt

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The phrase von mir aus may also be translated as "for all I care," "fine with me," "fine by me," or "as far as I'm concerned," but also as:

Wir wollen mit! Also gut, Jungs, von mir aus.

We want to come along! All right, boys, I don't mind.

Captions 15-16, Es war einmal... der Weltraum: Planet Omega

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The phrase nichts dagegen haben could be literally translated as "to have nothing against it," but in many contexts that is awkward. This is often a better solution:

Also, wenn du nichts dagegen hast, kann ich dieser Jackie ja mal 'nen Besuch abstatten.

So, if you don't mind, I can pay that girl Jackie a visit.

Captions 103-104, Die Pfefferkörner: Endspurt

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To summarize, the phrases nicht viel ausmachen (with a personal dative pronoun), von mir aus, nichts dagegen haben, and the adverb meinetwegen may all, depending upon the context, be translated as "don't mind."

Further Learning
Read the German Lesson Meinetwegen and von mir aus to go deeper into those terms. Then go to find some more examples on Yabla German to see other German words and phrases translated as "(I, you, we, they) don't mind."