How would you improve this backyard?

[Ricky Conti]

Hello BP!

Seeking some suggestions on how to best update this backyard to improve the space and make it more functional. The elevation is lower than the house to the right which currently causes water to pool after rainfall. Additionally, the large tree prevents sunlight from reaching much of the backyard. This appears to have prevented grass from growing and is attributing to the mud pit we have. The property is a half rented/half live in duplex purchased last summer and is in a B/C ish neighborhood.  Thank you for your thoughts!