Novice Topologist

You have entered into the confidence of the School of Topology and learned the basic tools and concepts of how to approach the study of space.

At 2nd level, you gain proficiency with Cartographer’s Tools.

Unless you have been moved while unconscious, you can not be lost except by magical means and always know how to retrace your steps. You always know the direction and distance to major landmarks in the area.

Spacial Sensitivity

After spending some time studying Topology, you gain a better understanding of space and its interconnectedness.

At 2nd level, nonmagical Difficult Terrain doesn’t slow your movement. Creatures that are behind half cover from you are considererd to have no cover and creatures that have three quarters cover from you are considered to have half cover.

As a bonus action, you can sense spacial disturbances (such as portals and teleportation effects) around you up to 1000 feet.

Competent Topologist

After careful study of the properties of space, you have gained enough understanding to shift it around and shape it in minor ways.

Starting at 6th level, when you cast a movement enhancing spell, it increases speed by another 10 ft. And when you cast a movement granting spell, it grants 10 ft. more movement. Also, add the Enlarge/Reduce spell to your spellbock, if it is not there already.

• When you cast Enlarge on a creature, the target's size quadruples in all dimensions, and its weight is multiplied by sixteen. This growth increases its size by two categories -- from Medium to Huge, for example. If there isn't enough room for the target to quadruple its size, the creature or object attains the maximum possible size in the space available. Until the spell ends, the target also has advantage on Strength checks and Strength saving throws,it has disadvantage on Dexterity checks and Dexterity saving throws, and it gains temporary hit points equal to twice your wizard level. The target's weapons also grow to match its new size. While these weapons are enlarged, the target's attacks with them deal 2d4 extra damage.
• When you cast Reduce on a creature, the target's size is quartered in all dimensions, and its weight is reduced to one-sixteenth of normal. This reduction decreases its size by two category--from Medium to Tiny, for example. Until the spell ends, the target also has disadvantage on Strength checks and Strength saving throws, advantage on Dexterity checks and Dexterity saving throws. The target's weapons also shrink to match its new size. While these weapons are reduced, the target's attacks with them deal 2d4 less damage (this can't reduce the damage below 1).

Expert Topologist

At 10th level, your powers over space have increased significantly.

Add the Misty Step spell to your spellbook, if it is not there already. Also, all your teleportation and transportation spells (Such as Misty Step, Thunderstep, Dimensional Door, etc…) have double the normal range.

Add the Leomund’s Secret Chest spell to your spellbook, if it is not there already. Also, all your dimensional spells’ effects can not be interrupted, intercepted, accessed, or lost, without your permission.

Master of Space

At 14th level, you have achieved the highest understanding of the Topology of Space and how to manipulate it. You break it down and put it together again according to your needs.

Add the Teleport spell to your spellbook, if it is not there already. And, when you cast it, add 20 to the DM’s d100 roll.

As an action, you can cast Far Step without using a spell slot or requiring concentration. You may do so a number of times equal to your Intelligence modifier (minimum 1). You gain expended uses once you complete a Long Rest.