This is a study to understand if taking VTX2735 is safe and effective in participants diagnosed with Recurrent Pericarditis (RP).

Cohort A will include approximately 10 participants and will consist of the following:

• A 30-day Screening Period (to see if a participant qualifies for the study)
• A 6-week Open Label Treatment Period - participant receives VTX2735 Dose A
• A 7-week Extension Treatment Period (if a participant meets criteria for extension treatment) - participant receives VTX2735 Dose A
• An 11-week Once Daily Treatment Period (if a participant meets criteria for this treatment period) - participant receives VTX2735 Dose B
• A 14-day Follow-Up Period

Cohort B will include approximately 20 participants and will consist of the following:

• A 30-day Screening Period (to see if a participant qualifies for the study)
• A 6-week Open Label Treatment Period - participant receives VTX2735 Dose B or C
• An 18-week Extension Treatment Period (if a participant meets criteria for extension treatment) - participant receives VTX2735 Dose B or C
• A 14-day Follow-Up Period

Cohort C will include approximately 20 participants and will consist of the following:

• A 30-day Screening Period (to see if a participant qualifies for the study)
• A 6-week Open Label Treatment Period - participant receives VTX2735 Dose D or E, and B
• An 18-week Extension Treatment Period (if a participant meets criteria for extension treatment) - participant receives VTX2735 Dose B
• A 14-day Follow-Up Period

Inclusion Criteria:

• Participants are male or female ≥ 18 years up to ≤ 75 years of age.
• Capable of giving signed informed consent and able to comply with the protocol
• Previously had an index (first) episode of pericarditis which met the criteria for an acute pericarditis event
• Ongoing symptomatic episode of pericarditis, or may have an episode of recurrent pericarditis in the next 4 weeks.
• CRP by local laboratory assessment prior to first dose of study treatment (participants with CRP ≤ 10 mg/L must be receiving corticosteroid treatment for RP and have evidence of pericardial inflammation)
• Pericarditis pain score ≥ 4 based on the 11-point NRS.
• Stable doses of NSAIDs, colchicine, and/or oral corticosteroids (if receiving these treatments)

Exclusion Criteria:

• Current or prior diagnosis of pericarditis that is secondary to specific prohibited causes, including but not limited to tuberculosis, blunt trauma, tumor, myocarditis, or systemic autoimmune diseases.
• History of clinically significant immunosuppressive disorder, autoimmune/autoinflammatory disorder, or primary or secondary immunodeficiency.
• Clinically important history of a medical disorder that would compromise safety or data quality, per the Investigator's judgment.