Mondrian is an open-source OLAP server written in Java. It is a relational OLAP (ROLAP) engine: it reads data from relational databases through JDBC, keeps aggregated results in an in-memory cache and answers multidimensional queries written in MDX. It also supports the XML for Analysis and olap4j interfaces. The code repository contains the core Java library and a Workbench, a desktop tool for creating Mondrian schemas. Developers embed it in reporting and analysis applications. It is a software component that you run yourself, not a hosted service.
Mondrian is released under the Eclipse Public License. Pentaho acquired the project in 2005, and Hitachi acquired Pentaho in 2015. The source code is published in the Pentaho organisation on GitHub, so the corporate steward is a US-based company. Because you deploy the engine yourself, you decide where it runs and where the data stays, and it can operate entirely on European infrastructure without any vendor hosting. Before building on it, check the repository for recent releases and activity, since the latest stable release listed on Wikipedia dates from 2017.