If a level has a padlock icon on it, you will need to unlock the level first before you are able to play it. New levels can be unlocked by playing earlier levels that are connected to them by dotted lines. Save a fish in any level to unlock the next level.
If you want to skip to a specific mode or level, you can do so from the settings menu.
Starting in version 1.2.2, you can also use the “Unlock All Modes” option in the settings menu to unlock the first level of the “Add”, “Connect” and “Multiply” levels. You can open the settings menu by tapping the screen once to bring up the settings button (a gear shaped icon) in the top left corner. Tap the settings button and then tap on “Unlock All Modes” near the bottom left of your screen.
Once you unlock all of the modes, you can use the "Unlock All Levels" option in the settings menu to unlock all of the levels in each mode. Please note that this option will only be available if you have already unlocked all modes.