Inclusion Criteria:  Aged between 18 - 69 years. Received a diagnosis of MS (any type of MS) at least 12 months prior to baseline assessment. Report cognitive problems, as determined by a cut-off score of 55 or lower on the oral SDMT Ability to give informed consent Able to commit to regular attendance in clinic, for up to 4 times a week for 4 weeks and follow up appointment eight weeks after the end of trial procedures.  Exclusion Criteria:  Diagnosed with depression or scores ≥15 on the Patient Health Questionnaire-9 Medical history of, or self-reported, seizures Neurological conditions (in addition to MS), e.g., brain neoplasm, cerebrovascular events, epilepsy, prior brain injury or brain surgery Contraindications to MRI scanning (identified by standard MRI safety screening questionnaire). Contraindications to TMS, including hairstyles or piercings that would impair magnetic transmission which cannot be altered to ensure effective intervention Frequent panic attacks which are likely to prevent regular attendance or participation in MRI/TMS procedures Prior TMS intervention Pregnancy MS relapse within the preceding 6 weeks Significant mobility problems if they are likely to preclude regular attendance in clinic, for up to 4 times a week for 4 weeks Involved with any other clinical trials involving medical procedures, interventions or treatment.