For an overview of Learning Tools Interoperability (LTI) and links to various resources including specifications see Learning Tools Interoperability on the IMS Global Learning Consortium's web site.
Direct links to the some of the IMS specifications (Implementation Guides) are:
For information on the content and interpretation of status messages, see Appendix A in IMS General Web Services WSDL Binding Guidelines.
OpenID Initiating Login from a Third Party
https://www.imsglobal.org/spec/security/v1p0/
https://github.com/blackboard/BBDN-LTI-Tool-Provider-Node
https://8gwifi.org/jwkconvertfunctions.jsp
Learning Tools Interoperability Core Specification IMS Final Release Version 1.3
https://metacpan.org/pod/Crypt::JWT
Learning Tools Interoperability (LTI) Assignment and Grade Services Specification 16 April 2019
Learning Tools Interoperability Names and Role Provisioning Services 16 April 2019
Learning Tools Interoperability (LTI) Deep Linking Specification 16 April 2019
Learning Tools Interoperability Advantage Implementation Guide 16 April 2019
https://andyfmiller.com/2018/12/27/using-swagger-to-explore-the-lti-advantage-api/
https://advantageplatform.azurewebsites.net/swagger/index.html
Tool consumer and provider emulators were developed as part of the ceLTIc project. They can be found at provider and consumer.
And supporting more recent features at: saLTIre.
Additional tools, including an OAuth sandbox can also be found via the IMS Learning Tools Interoperability: Testing Integrations page.
Sakai LTI Unit Tests has a test tool consumer and a test tool provider and links to the PHP code.
A tool provider, for versions up to 1.2, that shows all of the launch parameters it receives by type (required, recommended, etc.) and the XML sent and received in the Outcomes Management Service grade exchange can be found at NetKnowledgy LTI Tests.
OAuth:
Links to sample code can be found at sample code.
Additionally: