Connections: Stones and groups can be connected solidly with no way to break apart or loosely but farther reaching with more possibilities. Whether you want to have solid connections and loose connections all depends on the local and global situation of the board. For example, loose connections can actually be quite solid along the edge of the board because the edge can be used to your advantage.
Two Eyes: An eye is an empty liberty inside of a group of stones. For a group to stay on the board unconditionally or be alive (it cannot be captured), it must have two separate empty liberties inside of it or two eyes.
Life and Death: The study of gaining life for your groups or killing your opponent’s groups is called life and death. Life and death is usually considered the most important subject to study at beginner levels, but remains extremely important all the way to professional levels. Much of it is based on reducing what is called eye space (space to make two eyes with) and turning what could be two eyes into one or no eyes. The example below is only the very beginning. Practice, practice, practice!
Capture Race and Seki: When adjacent opposing groups are both unable to live and the outcome is dependent on who can capture first, a capture race is created. It becomes a race to take the liberties of your opponent’s group before he can take the liberties of your’s. In certain situations, the capture race can end in a draw with neither player able to capture the other, yet neither group has two eyes. This is called a seki, or dual life. Remember to count your liberties at all times in fights!
Tesuji: Specific arrangements of stones can lead to unique tactical plays that can benefit you greatly if you can read them out. A tesuji is best known as a clever play, skillful move, or best move in a local situation. Always be on the lookout for what works and what doesn’t work.
Shape: Go can be a game of patterns, so we can see that certain shapes in stones often lead to better results than others (there are always exceptions, so it is important to analyze the situation carefully at all times). What is good shape and what is bad shape? Being able to answer this confidently comes with experience, but as an introduction, it is often seen shapes that produce eyes or are flexible and efficient are good shape and bulky clumps of stones are bad shape.