- First, some more recent work, mostly overviews.

1. The following is the most recent overview of the field I'm aware of:

Inductive logic programming at 30 (Cropper et al, 2020)

https://www.doc.ic.ac.uk/~shm/Papers/ilp30.pdf

2. And a slightly shorter version of the same paper that summarises new trends:

Turning 30: New Ideas in Inductive Logic Programming (Cropper et al, 2020)

https://www.ijcai.org/Proceedings/2020/0673.pdf

3. Here's a short introduction to the relatively new ILP direction of learning Answer Set Programming:

Inductive Logic Programming in Answer Set Programming (Corapi et al, 2011)

https://link.springer.com/chapter/10.1007/978-3-642-31951-8_...

4. This is an overview of Meta-Interpretive Learning (MIL), a new approach to ILP that overcomes many difficulties of earlier approaches (Full disclosure: my own work is on MIL, though not the article linked):

Meta-Interpretive Learning: achievements and challenges (Stephen Muggleton, 2017)

https://www.doc.ic.ac.uk/~shm/Papers/rulemlabs.pdf

5. And this is a (short vesion) of a paper on δILP, a neural-net based ILP system:

Learning Explanatory Rules from Noisy Data (Evans and Grefenstette, 2018)

https://www.ijcai.org/Proceedings/2018/0792.pdf

- Next, some earlier work that is still relevant:

6. This is the inaugural paper of the field, that first named it (a little heavy reading though):

Inductive Logic Programming (Stephen Muggleton, 1990)

https://www.doc.ic.ac.uk/~shm/Papers/ilp.pdf

7. Here's an early paper on predicate invention, an important technique in ILP (only recently fully realised via MIL):

Predicate Invention in ILP - an Overview (Irene Stahl, 1993)

https://link.springer.com/chapter/10.1007%2F3-540-56602-3_14...

8. And an early overview of learning recursion (and performing predicate invention) that also lists several early ILP systems:

Inductive synthesis of recursive logic programs:achievements and prospects (Flener and Yilmaz, 1999)

https://core.ac.uk/download/pdf/82810434.pdf

That should be enough to get you started. I recommend reading in the order I linked to the various articles. I tried to give links to documents that I know can be read for free.

Unfortunately most of the material on ILP is either in scholarly articles, or, where there are textbooks, they tend to be older. That sounds bad, but there has been much new work recently with several new approaches.

Let me know if you're looking for more specific information. See my signature for contact details- I'm happy to answer emails about ILP :)