This volume contains the papers presented at UNIF 2018: The 32nd International Workshop on Unification held on July 7, 2018 in Oxford.

UNIF 2018 was affiliated with the Third International Conference on Formal Structures for Computation and Deduction FSCD 2018, part of the Federated Logic Conference FLoC 2018. 

There were 10 submissions. Each submission was reviewed by at least 3, and on the average 3.2, program committee members and external reviewers. The committee decided to accept 8 papers for presentation and 2 for short presentation. The program also includes 2 invited talks:

Silvio Ghilardi 
"Handling substitutions via duality"

Adrià Gascón 
"Compressed Term Unification: Results, uses, open problems, and hopes"

We would like to thank all members of the program committee and the subreviewers for their high quality reviews and discussion held on the EasyChair platform that assured the scientific standard of UNIF in its 32nd edition.   

Finally, we would like to thank the UNIF Steering Committee and the FSCD and FLoC scientific and organising team for the support before and during the workshop.