diff --git a/book/source/08-signing_components.md b/book/source/08-signing_components.md
index 526be8b..885295b 100644
--- a/book/source/08-signing_components.md
+++ b/book/source/08-signing_components.md
@@ -6,22 +6,28 @@ SPDX-License-Identifier: CC-BY-SA-4.0
 (component_signatures_chapter)=
 # Signatures on components
 
-In this chapter, we'll consider OpenPGP signatures that apply to components. That is, signatures that apply to:
+In this chapter, we'll look into OpenPGP signatures that apply to components of certificates. That is, signatures that apply to:
 
-- Component keys (primary keys or subkeys), or
+- Component keys (primary keys or subkeys) and
 - Identity components (User IDs or User attributes).
 
-This chapter adds a lot of detail to the material we discussed in the {ref}`certificates_chapter` chapter. Signatures on components are a crucial mechanism for forming OpenPGP certificates (which combine component keys and identities, via signatures on those components).
+This chapter adds detail to material we discussed in the {ref}`certificates_chapter` chapter. Signatures on components are a crucial mechanism for forming OpenPGP certificates and .
 
-Additionally, signatures on components play a crucial role for authentication of identities. Mechanisms for decentralized authentication are one of OpenPGP's core strengths, we'll look into how they work.
+## Self-signatures: Forming certificates and life-cycle management
 
-Finally, signatures on components are also a central mechanism for life-cycle management of OpenPGP certificates and their components. This includes defining or changing expiration dates, or issuing revocations, for certificates or their components.
+*Self-signatures* are issued by the certificate's owner, using the primary key of the same certificate.
+ 
+Signatures on components are also a central mechanism for life-cycle management of OpenPGP certificates and their components. This includes defining or changing expiration dates, or issuing revocations, for certificates or their components.
+
+## Third-party certifications: Encoding authentication
+
+Additionally, signatures on components play a crucial role in the authentication of identities. Mechanisms for decentralized authentication are one of OpenPGP's core strengths, we'll look into how they work.
 
 ## Self-signatures and third-party signatures
 
 There are two important scenarios to distinguish:
 
-- *Self-signatures*: Issued by the certificate's owner, using the primary key of the same certificate.
+
 - *Third-party signatures*: Issued by a key that is part of a different certificate.
 
 ### Meaning differs between self- and third-party signatures