Applying a conscious set of processes to the acquisition, classification, development, repurposing and sharing of new, personally-applicable knowledge.
Grundspenkis 2007
>a collection of processes that a person uses to gather, classify, store, search, retrieve and share knowledge in their daily activities
-- Grundspenkis, J. (2007), "Agent based approach for organization and personal knowledge modelling: knowledge management perspective", Journal of Intelligent Manufacturing, 18 (4): 451–457 journal 
-- via wikipedia
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One of the leading proponents of PKM is Harold Jarche through his Seek Sense Share framework..
PKM as commonly discussed is intrinsically about the use of internet-enabled Tools for Personal Knowledge Management, and the connection of ideas from different sources, so is therefore an instance of Connectivism.
The Sense-making aspect of PKM also involves elements of Constructivism
Many practitioners draw from multiple sources and disciplines, so PKM is also often an example of Integrative Learning.
Different tools favour different modalities, called out by various writers as the difference between "Garden" (aka State Mode) and "Stream" (aka Stream Mode).
A common challenge for all forms of knowledge management, including PKM, is how to go about Categorising Things
As well as relating theories of learning to PKM, we might also consider Contributions to PKM from NeuroScience.