I do not claim to know everything, in fact, I know very little compared to the things I don't know, the things I don't know I don't know and the things I thought I know but indeed I don't. However, there are some areas I am confident to say that I have knowledge on.
Engineering:
Vibration-based Energy harvesting using piezoelectric material (my PhD thesis)
Mechanical vibrations, resonance (modeling and analysis)
Mechanical dynamics, kinematics, solid mechanics (modeling and analysis)
Mechanical designs and producing engineering drawings
Aircraft aerodynamics (my undergraduate summer research)
Unmanned Aerial Vehicles (my undergraduate final year project, I was the team leader of the 4-man team)
Electrical AC and DC circuit analysis
AC-DC and DC-DC converters
Micro-controller programming (most experience in AVRs, ARMs processor)
Micro-controller architectures
Analog and digital circuit designs
Inductor designs
PCB designs
Understanding the working principles of most sensors and actuators
Mathematics:
Calculus
Vector calculus
Partial differential equations
Eigenvectors, Eigenfunctions and Eigenvalues
Vector space and approximation theory
Taylor and Fourier series (which are derived from approximation theory)
Fourier and Laplace transform
Computer skills:
Linux and windows operating systems
General applications (office, graphics etc) in both OS
Matlab (modeling and data processing)
Labview (configuring instrumentation)
Solidworks (mechanical designs and drawings CAD)
Altium (PCB designs CAD)
SVN subversion control
Latex (producing professional documents)
C, C++ and C# programming languages
Object oriented programming
Visual Studio (for graphical user interface programming)
XML database
Genetic algorithm
Neural networks
Hands on skills:
Mechanical workshop (milling machines, lathe, gas cutting, welding etc, I worked in an excavator company to make parts and modify buckets over a summer)
Instrumentation setup (for experiments, data acquisition, automatic testing etc, instruments I often use include laser vibrometers, National Instruments, electromagnetic shakers, accelerometers)
PCB making (I use lithographic technique to make double layer PCBs that have trace width down to 10mil)
Leisure:
Acoustic guitar (play classical music)
Skiing
Swimming
Squash
Gym
Things that I am trying to improve:
Body muscles
Oral communication skills
Writing skills
Leaderships
Social skills
Things that I'm currently learning:
Building commercial websites using content management software Drupal
Running small businesses
Basic accounting
Flying an RC electric helicopter
International trading and politics
Investing
Things that I plan to learn in the near term:
SQL and mySQL database
Javascript for web development
Marketing