Recent identification of network-level organizing principle and memory-encoding units in the hippocampus has allowed real-time patterns of memory traces to be mathematically described, intuitively visualized, and dynamically deciphered. Any given episodic event is represented and encoded by the activation of a set of neural clique assemblies, which are organized in a categorical and hierarchical manner. This hierarchical feature-encoding pyramid is invariantly composed of the general feature-encoding clique at the bottom, subgeneral feature-encoding cliques in the middle, and highly specific feature-encoding cliques at the top. This hierarchical and categorical organization of neural clique assemblies provides the network-level mechanism the capability of not only achieving vast storage capacity, but also generating commonalities from the individual behavioral episodes and converting them to the abstract concepts and generalized knowledge that are essential for intelligence and adaptive behaviors. Furthermore, activation patterns of the neural clique assemblies can be mathematically converted to strings of binary codes that would permit universal categorizations of the brain's internal representations across individuals and species. Such universal brain codes can also potentially facilitate the unprecedented brain-machine-interface communications.