Motivated by Shannon's model and recent rehabilitation of self-supervised artificial intelligence having a "World Model", this paper propose an unified intelligence-communication (UIC) model for describing a single agent and any multi-agent system. Firstly, the environment is modelled as the generic communication channel between agents. Secondly, the UIC model adopts a learning-agent model for unifying several well-adopted agent architecture, e.g. rule-based agent model in complex adaptive systems, layered model for describing human-level intelligence, world-model based agent model. The model may also provide an unified approach to investigate a multi-agent system (MAS) having multiple action-perception modalities, e.g. explicitly information transfer and implicit information transfer. This treatise would be divided into three parts, and this first part provides an overview of the UIC model without introducing cumbersome mathematical analysis and optimizations. In the second part of this treatise, case studies with quantitative analysis driven by the UIC model would be provided, exemplifying the adoption of the UIC model in multi-agent system. Specifically, two representative cases would be studied, namely the analysis of a natural multi-agent system, as well as the co-design of communication, perception and action in an artificial multi-agent system. In the third part of this treatise, the paper provides further insights and future research directions motivated by the UIC model, such as unification of single intelligence and collective intelligence, a possible explanation of intelligence emergence and a dual model for agent-environment intelligence hypothesis. Notes: This paper is a Previewed Version, the extended full-version would be released after being accepted.