Formal:
* Bardzo dziękuję. (Bah-rdzo dzen-kyeh) - This is the most common and formal way to express gratitude.
* Serdecznie dziękuję. (Ser-detch-neh dzen-kyeh) - This is a slightly more heartfelt and formal way to say thank you.
* Składam serdeczne podziękowania. (Skwa-dam ser-detch-neh pod-zee-en-kwan-ya) - This is the most formal way to say thank you, literally translating to "I offer heartfelt thanks."
Informal:
* Wielkie dzięki! (Vyehl-keh dzen-kee!) - This is a very casual and friendly way to say "thanks a lot!"
* Ogromne dzięki! (O-grom-neh dzen-kee!) - This is similar to "Wielkie dzięki" but even more emphatic.
* Dziękuję Ci bardzo! (Dzen-kyeh tsee bah-rdzo) - This is a slightly more informal way to express gratitude, using "Ci" which translates to "you."
Other options:
* Dziękuję z całego serca. (Dzen-kyeh z tsa-leh-go ser-tsa) - This translates to "Thank you from the bottom of my heart."
* Jestem bardzo wdzięczny/wdzięczna. (Yes-tem bah-rdzo v-dzen-chni/v-dzen-chna) - This translates to "I am very grateful."
The best option to use will depend on the specific context and your relationship with the person you are talking to.