Question: Yennefer and Geralt are supposed to have an especially close romantic relationship. Yet I through the Witcher games, Geralt freely sleeps with a number of other female characters.

I cannot recall Yennefer ever discussing how she feels about this during the games. Do we ever get an insight on her opinions about Geralt's promiscuity?

Answer: 
At the very least, her actions give us insight of her disapproval. That said, Geralt and Yennefer's relationship is not necessarily a natural one.

Geralt and Yennefer's Relationship
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In Witcher lore, Yennefer first appears in "[The Last Wish](http://witcher.wikia.com/wiki/The_Last_Wish_(short_story) "\"The Last Wish\" (short story) @ Witcher Wiki")". Without the need for unnecessary spoilers, Geralt frees a djinn, and is granted three wishes. Towards the end of the story, Geralt uses his last wish *"so that Geralt and Yennefer, despite their many differences, could not live without each other."*

The love affair is only lightly referenced during the first two games. To quote Geralt, *"My amnesia prevents me from remembering our relations in the past, but I have the impression I once loved a sorceress, deeply..."*. In the second game, it only comes to light *at the end* that Yennefer may actually be alive. It is suggested that she may also suffer amnesia.

While you can woo other woman, during Witcher 3, Yenneffer is mostly still under the spell of the djinn. Further towards the end of the game, Yenneffer will ask you to help her trap another djinn, during the quest The Last Wish. She intends to use the djinn to remove the spell of the previous djinn, to find out wether her and Geralt truely love eachother. If you complete the quest, you have the option to tell Yennefer you still love her, or tell her you do not. 

It is clear that she still has feelings for Geralt. If you choose to tell her you no longer have feelings, the quest log reveals that *"The truth came as a brutal shock to Yennefer, though she was not the kind to let this show."* If you choose to tell her you still love her, there is a high probability that you will be moving towards the "Yennefer ending".

Reaction to promiscuity
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If you try to romance both Yennefer *and* Triss, you will be treated to a scene before the search for the Sunstone, where they both try to seduce Geralt, together. Unfortunately, it is a ruse, and the two chain Geralt to a bed, and leave him there, naked. From that point on, conversing with either character make it clear that they have lost all interest in pursuing a romance with Geralt.

Further speculation
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There does not appear to be any reaction to other cases of promiscuity, either from using brothels, or romancing DLC characters.

Within scope of the Arqade, it is up to you to make your own assumptions on whether these other cases were simply unknown to Yennefer, or whether she was happy with Geralt exploring alternate sexual partners, but not alternate romantic partners. There is also the potential argument that all other encounters are simply not cannon to the main story, and simply available for the purpose of providing player choice.

Further information
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As you likely know, the three The Witcher games are based off a a series of like-named novels and short stories. While asking solely in context of the games is permitted on this site, we have an alternate Stack Overflow site that will take questions in regards to the entire Witcher series, including video game, TV series and novels. If you would like to explore the possibility of further insight in the novel series, [SciFi Exchange](https://scifi.stackexchange.com/ "SciFi Stack Exchange (questions regarding SciFi & Fantasy)") would be a good place to ask.
I'll add a few more information from the books: Yennefer asks once Geralt "has he been faithful to her", for which he replies "Yes, I've been always thinking only about you", which seems to satisfy her. She seems to get a bit upset with Triss having a brief affair with Geralt, but she settles the matter after having a "strong talk to" with her friend.

Saying all that Yennefer is not saint herself: in the "A shard of ice" story she and Geralt met her old lover, a mage called Istredd.

> 
> "My deep friendship with Yennefer," continued Istredd, "started quite some time ago, witcher. It has long been a friendship without obligations, based on long or short, but more orless regular, periods spent with one another. This type of casual relationship is often practiced amongst our profession.
> 
> 
> 

Geralt and Istredd have at one stage a heated discussion about who is better suited as her partner. The mage points to his wealth and status and says that Geralt is just a "plaything". Annoyed Geralt replies:

> 
> The witcher thought for a moment and decided to finish it.
>  "Because," he burst out, "Last night she made love with me and not you."
>  Istredd picked up the skull, stroking it. 
>  "A ha," the magician said slowly, "Fine. Well. She made love with me this morning. 
> 
> 
> 

In other words, it seems that both Geralt and Yennefer are people for whom **casual** sex with other partners is not a barrier for a true romantic relationship.