Swingtum stands for Swing and Momentum. A Swingtum Theory of Intelligent Finance is presented here in order to provide a scientific and engineering foundation to professional swing trading and momentum trading. The origins of Swingtum theory naturally go deep into the empirical professional technical analysis, fundamental analysis and strategic analysis, and academic quantitative analysis including financial mathematics, econophysics and computational intelligence. The central perspective of Swingtum theory is the pervasive existence of multilevel swings and abrupt momentum moves in the market prices, business fundamentals, mass psychology, and even the news flow. The dualism of swing versus momentum may resemble the wave-particle dualism in quantum mechanics, however with much higher nonlinearity and sophistication of human traders as building elements of the markets. This view forms the Swingtum Market Hypothesis, which is closer to the reality than Efficient Market Hypothesis and Fractal Market Hypothesis are. Swingtum theory models the markets with two parallel and intertwining lines of thought: the multilevel swings and momentums of a target market, and the influences from interrelated markets and the surrounding economic environment. The two lines are then unified into a comprehensive framework - Super Bayesian Influence Networks (SBIN) consisting of many Probability Ensembles of Neural Networks (PENN).