1. An assignement of a right is a transfer of an existing right from one person to another.
a) At common law choses in action (all personal rights of property which can only be claimed or enforced by action, and not by taking physical possession) were not assignable.
b) Statutory 'exceptions':
aa) Negotiable instruments have become freely assignable by the custom of merchants, most other choses in action have been made expressly so by various statutes, such as copyright and patent rights.
bb) Contract rights other than negotiable instruments: Law of Property Act 1925. Express notice must be given to the debtor.
c) Equity: all equitable rights are freely assignable. The Court of Chancery would even support the claim of an assignee of a purely 'legal' right (complicated procedure, now superfluous)! However, equitable assignments can still be made according to rules which are less exacting (no formalities) than the rules laid down in the Law of Property Act 1925.
d) Contract rights that are not assignable: bare rights of action; rights of a personal nature (personal services).

2. Rules governing assignments of rights generally (whether statutory or equitable)
a) If the assignee fails to give notice of the (equitable) assignment to the debtor, the latter is entitled to discharge his liability by paying the assignor himself, or by paying any other assignee who gives him notice.
b) The assignment of equitable rights must be communicated to the debtor (i.e. trustee) in writing (not the 'equitable assignment' as mentioned above!).
c) The assignee always takes subject to any rights (such as rights of set-off) which the debtor may have against the assignor ('Nemo dat quod non habet'). The assignor cannot give the assignee a better right than he himself has.