Subdivision (a) sets the default and distinguishes two kinds of liability. All partners are liable jointly and severally for everything chargeable to the partnership under §§ 24 and 25 - the sections dealing with wrongful acts and misapplied property. For all other debts and obligations of the partnership they are liable jointly, and any partner may in addition enter into a separate obligation to perform a partnership contract. In a general partnership, personal liability is the rule: the firm's creditors can reach the partners.
Subdivision (b) creates the exception that makes registered limited liability partnerships worth registering. No partner of a registered LLP is liable or accountable, directly or indirectly - including by indemnification or contribution - for the debts, obligations or liabilities of the partnership or of each other, whether in tort, contract or otherwise, incurred while it is a registered LLP, solely by reason of being a partner or acting in that capacity or participating in the conduct of the business.
Subdivision (c) puts the crucial limit on that shield: each partner, employee or agent of a registered LLP remains personally and fully liable for any negligent or wrongful act or misconduct committed by that person, or by anyone under their direct supervision and control, while rendering professional services. The LLP protects a partner from the acts of others, not from their own. Subdivision (d) lets a majority of partners agree that all or specified partners will be liable for all or specified debts, with the modification or revocation of such an agreement having no retroactive effect. Subdivision (e) preserves the partnership's own liability out of partnership assets, and subdivision (f) keeps the shield in place for debts incurred while the LLP status existed even after withdrawal, revocation, dissolution or winding up.