How did Charles Sanders Peirce distinguish deduction, induction, and abduction?

Charles Sanders Peirce, an influential American philosopher and logician, sought to integrate three distinct forms of inference into the formal study of logic: deduction, induction, and abduction.1

Peirce distinguished these methods based on their logical function and their relationship to knowledge:

• Deduction: Peirce recognized this as the traditional form of mathematical or deductive logic, which draws necessary conclusions from established premises.1
• Induction: He viewed this as a method of testing hypotheses by examining instances to reach a general conclusion, which is central to the logic of science.1
• Abduction: Also referred to by Peirce as "retroduction," this is the process of forming and accepting a hypothesis on probation to explain surprising facts. Unlike deduction, which derives consequences, abduction is the creative act of guessing or questioning to generate an explanatory hypothesis.12

Peirce’s lifelong ambition was to establish these three modes as clearly distinguished yet positively related components of logic, arguing that a logician must understand the methods of all sciences to effectively employ these reasoning strategies.1