diff --git a/index.md b/index.md
index ec82552..5c6b238 100644
--- a/index.md
+++ b/index.md
@@ -745,7 +745,7 @@ This section slightly intersects with the one on representation theory (especial
 
 **[Introduction to Analytic Number Theory](https://www.amazon.com/Introduction-Analytic-Number-Theory-Apostol/dp/0387901639/ref=sr_1_1?crid=2D18GWR38K1FZ&dib=eyJ2IjoiMSJ9.swV8CUeh7U0WpIy7CrNJ4_SWrNEhD2xpVKyZceBtORXTp2vDLZtq0U6PJeVlI_irKnoqMm7v2cEeCVHEuYs6zjMgu6CV3dD4kmRLrM5MDnwSMwc6Y32Xmt_8s7jqmk_VpuVhGTGDmlvBN522dhWyXwVsVTS1usTBVxaX6jYmmmsdCXTvWmGectxTzhPRvsRmctAC5Dncd7-DoUwhLTViWd18_L8-QC5iY8n6prjugo1By2UyZ6bndmkwFSulMW-Tty3ePop1ewP5ce6e8p4YZw.Lh2BB7n6cfPhX7KUaIhYT0szFESDBLGK8vvVc4NhUBM&dib_tag=se&keywords=apostol+analytic&qid=1711146881&sprefix=apostol+analyti%2Caps%2C172&sr=8-1)**, *Tom M. Apostol*
 
-<img src="/learn-mathematics/img/.jpg" alt="" width="200px"/>
+<img src="/learn-mathematics/img/apostol.jpg" alt="Apostol" width="200px"/>
 
 **[Multiplicative Number Theory](https://www.amazon.com/Multiplicative-Number-Theory-Graduate-Mathematics/dp/0387950974/ref=sr_1_1?crid=3NFJTKZOWRGVP&dib=eyJ2IjoiMSJ9.gIAr-YN4V3hb29v6M6UvRQKMXQF3CSStj5W1BRcObD6G6o7_e8PDg7QIj5SOBmGyX6w9WFRTdxPijCuK-JPwXSKlo7RInYqrvg3OJYsCabJS_ZV3Q1k538cUSluxZsBDw-oHZoy0OgS787UXETehjLq5cedhl0Gpk0ngIzSHE6xmlbL9Ly-AsflUlbCEzhDmxbx51X0fZ4dA3VO6WSofVQ8UwjoSSQcAq9fRnB2Vc_c.gS9Ct5OF9Od-7bJURll2K6TAzLmsih7OvoQ-imKTcpw&dib_tag=se&keywords=multiplicative+number+theory&qid=1711146920&sprefix=multiplicative+number+theor%2Caps%2C191&sr=8-1)**, *Harold Davenport*
 
@@ -773,7 +773,7 @@ This section slightly intersects with the one on representation theory (especial
 
 **[Algebraic Number Theory](https://www.jmilne.org/math/CourseNotes/ANT.pdf)**, *J.S. Milne*
 
-<img src="/learn-mathematics/img/milne-ant.jpg" alt="Milne ANT" width="200px"/>
+<img src="/learn-mathematics/img/milne-ant.png" alt="Milne ANT" width="200px"/>
 
 **[Algebraic Number Theory](https://www.amazon.com/Algebraic-Number-Theory-Graduate-Mathematics/dp/0387942254/ref=sr_1_3?crid=15OSO20NR0MRB&dib=eyJ2IjoiMSJ9.LuU3_wKqvKgO9AxKBlSNylSp7yXC3gxIpJPF-GKnrfvGsrFyR51UPfFXp4urRc2uAixdQSIKCiBHSz9DF88d7EWfBjE3APOgIjeCOHrdQfmwXvY2G13AFdj174jOQimuW7QuFia-3deP4ffNNrzSiKKdPqBXsCjvp1MdWSmoACKzqruAEq_dj85vjqT_2mb8fueiMwv79RGWiMEy5vCnQhJAHRzGRUnu7E2H_RxC3IbVpRnKxpfRggqogON_x4ay6HKk_6AcCb4DR8ImvSx_OhHCtb9oPNWivFJKlKgMTlE.nOslLyCq6Q4P1J79RCMCaRWb0fBZg9_EKmlPjE1IlFM&dib_tag=se&keywords=algebraic+number+theory&qid=1711147200&sprefix=algebriac+number+theor%2Caps%2C172&sr=8-3)**, *Serge Lang*