FCC Rules Parts 15 and 18 specify limits on stray emissions from your wireless power transfer system. These limits are very low, and are a surprise to many entering the wireless power transfer discipline.
Learn classical electromagnetics. One good text: "Static and Dynamic Electricity" by William R. Smythe, third edition 1989, Hemisphere Publishing Company.
Purchase a copy of the "ARRL Handbook" from arrl.org, for its discussion of electromagnetics fundamentals.
Look up the properties of coupled tuned circuits. One good text: "Radio Engineering" by Frederick R. Terman, second edition 1937, McGraw-Hill. This may be hard to find, as McGraw-Hill dropped all their classic texts some years ago. The physics community has recently gotten excited about coupled tuned circuits. What radio people call "critical coupling", physicists call an "exceptional point". Resonant inductive coupling was used in intermediate-frequency transformers in vacuum-tube radios in the 1930s through 1970s.
Below, I list some publications of one group working in this area.
http://arxiv.org/abs/physics/0611063, paper given at 2005 Industrial Physics conference in San Francisco: Aristeidis Karalis, J. D. Joannopoulos, and Marin Soljacic, "Wireless Non-Radiative Energy Transfer", Center for Materials Science and Research Laboratory of Electronics, MIT.
Andre Kurs, Aristeidis Karalis, Robert Moffat, J. D. Joannopoulos, Peter Fisher, and Marin Soljacic; "Wireless Power Transfer via Strongly Coupled Magnetic Resonances"; Published online June 7, 2007; 10.1126/science.1143254 (Science Express Research Articles).
http://www.sciencemag.org/cgi/data/1143254/DC1/1 contains supporting online material from Science paper in PDF format, including photos of operation. Enlarging figure 4 on page 6 discloses that their oscillator is built around an 833A power triode and a vacuum variable capacitor. The tube puts out as much light as the lighbulb does. Kurs, etal, state that their system puts out an amount of stray radiated power, which is much more power than the FCC rules permit, but they don't show awareness of the FCC limits in their paper.
See US patent applications 20070222542 and 20080278264.
