This volume contains the papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford.

Linearity has been a key feature in several lines of research in both theoretical and practical approaches to computer science. On the theoretical side there is much work stemming from linear logic dealing with proof technology, complexity classes and more recently quantum computation. On the practical side there is work on program analysis, expressive operational semantics for programming languages, linear programming languages, program transformation, update analysis and efficient implementation techniques.

Linear logic is not only a theoretical tool to analyse the use of resources in logic and computation. It is also a corpus of tools, approaches, and methodologies (proof nets, exponential decomposition, geometry of interaction, coherent spaces, relational models, etc.) that were originally developed for the study of linear logic's syntax and semantics and are nowadays applied in several other fields.

The aim of this Joint Linearity and TLLA workshop is to bring together researchers who are currently working on linear logic and related fields, to foster their interaction and provide a forum for presenting new ideas and work in progress, and to enable newcomers to learn about current activities in this area. The main goal is to present and discuss new trends in Linear Logic and its applications, by means of tutorials, invited talks, open discussions, and contributed talks. New results that make central use of linearity, ranging from foundational work to applications in any field, are welcome. Also welcome are more exploratory presentations, which may examine open questions and raise fundamental concerns about existing theories and practices.

The programme of the workshop consists of 18 papers and four invited talks. More information about the workshop can be found on the workshop web page: http://lipn.univ-paris13.fr/TLLALinearity18/

We would like to thank all those who contributed to Linearity/TLLA  2018, particularly the invited speakers, programme committee members and local organisers. EasyChair was used to manage the reviewing process and the generation of the preproceedings.